Have you ever posted on social media and wondered how come I don't get as many likes as I see other people do? Well, you have to understand how the algorithm for most social media platforms work. You see in the newsfeed, in the home screen, when you log in social media and just browsing, what you see are the popular posts. You don't see the 99% of the other posts that were also posted today that didn't get popular, that didn't get as many likes. So you think you're the only one getting one or two likes or whatever might be for you, whatever low means for you. Is it zero? For some people who have a bit of an audience, maybe a hundred likes is low for them because they're usually used to getting several hundred or thousands or whatever and now they're only getting a hundred and now they're wondering what happened and they're getting discouraged. For those of us who are just starting out, maybe low is just a few likes or zero likes or something, but if you're wondering, if you're comparing yourself with the other posts and how many likes they're getting in the home feed, you are comparing your normal stuff with everybody else's most popular hits. And the fact is, if you keep posting stuff, eventually you have a few things here and there that also become popular or at least get more likes than you typically do and but if you keep posting, hoping for those popular things or you keep posting wanting to be as popular as what you're seeing in the home feed, you are always going to be in a losing game because like I said, you're just seeing everyone's popular stuff. Okay, so you have to realize a couple things. One, when you are posting for likes, when you are concerned about likes and comments and shares or whatever it may be, what's happening is that you're giving a bit of your power away each time and the more of your power you give away, the more of your uniqueness you give away. You have got to create content, not caring whether people are going to like it or not, but do it because it is your truth, because it is something you feel is important to express because otherwise you won't get to express it and that's what you're here to do in this life is you're here to express what you believe is important, what you have come through, the experiences you've come through, the insights you have, the peak experiences you have, the problems you've solved, the things you've helped, otherwise, the things that you genuinely believe are going to be helpful for others, whether or not they then find that to be helpful, it is your calling to share it anyway. And if you do share it from there, every time you share it from there, you are doing it in your authentic power and you are going to become, your content is going to become unique, not like everybody else's. If everyone is just, if you're just trying to post based on what's going to get more comments and shares and likes, then you become like everybody else's comments and you know, you're everybody else's content. So let me offer you a simple kind of several steps to do it when you're posting on social media and doing it authentically, okay? Step one is to take a moment, instead of just posting the thing, take a moment and reconnect to the source where you find your self-worth, because your self-worth cannot be tied to how many likes you get for this or for that. If it is, you're in trouble and you are going to always be giving away your power and you can't ever build a presence based on your real authenticity, okay? So step one is whatever practice, spiritual practice, personal growth practice you need to do to just take, for me, it just takes 30 seconds to do that. You don't have to spend a long time doing it. Just spend just just a few seconds, a few minutes, reconnect and reminding yourself that you don't need anybody else's approval. Okay? Step one. Step two is to post based on what you believe is true, what you believe is important regardless of what anyone else is going to think about it, okay? Because that is going to be the most, you sometimes when you post things and people don't get it yet, you're just ahead of your time. You really are. The world, your network doesn't understand it yet, but one day as you grow your brand and your presence, people are going to look back on some of your earlier stuff and go, wow, she or he was wow, you know, pretty ahead of, ahead of what where society was amazing, right? So step one, reconnect with your source. Step two is to post your authentic truth. Not, ooh, I'm gonna post this because it's gonna get a lot of likes and shares and stuff like that because you're just giving your power away and you're gonna become tied to needing to live by other people's approval, which is, which is going to be a recipe for anxiety, discouragement, depression, etc. So don't do it, okay? Reconnect to your source, post from your authentic truth, post your authentic truth, and three, after you post, after you do your social media thing, you post your content, step away and do something else.  Did anyone like it yet?  You're giving your power away. Okay, you're giving your power. You're tying your sense of acceptance and happiness based on what other people are saying about your content. So that's step three, step away, do something else. Okay? Step four, after enough space, okay? Then come back and check the metrics, but when you're checking the metrics, you're not checking to see, ooh, do people like me? You're comparing based on your other posts and seeing, is this topic that I've said understandable by other people? Is it understandable by other people? Are people resonating with it? And then you have a choice to say, if people are resonating with it, maybe I should think about doing more stuff like that in the future if it's resonant with my authentic truth, not because I'm trying to be more light. So I hope this is helpful for you to create more authentic social media content. I wish you well.


Welcome dear learners. My name is Chayani Kasinapati and I am from Maniram Devan School of Management. The present video is on the unit contemporary issues in management and in this part of the video that is part one of the unit we will discuss about the concepts like meaning of conflict, the types of conflict and describe the conflict management and in the next part of the video we will discuss about stress management, the sources of stresses and the stress management strategies. Now let us discuss about the meaning of conflict. Conflict is a disagreement between two or more parties such as individuals, groups, departments, organizations or countries who perceive that they have incompatible concern. Conflict exists whenever an action by any party is perceived as interfering with the goals or needs or actions of the another party. So conflicts can arise from several reasons. Some of them are mentioned in this video. They may be incompatible goals and differences in the interpretation of facts, the negative feelings, variations in values and philosophies then disputes over shared success. So conflict is neither good nor bad. The outcome of a conflict is the criteria for determining whether the conflict is functional that is a conflict that supports organizations goal or dysfunctional like a conflict that prevents an organization from achieving its goal. So that is whether it has positive or negative outcomes for concerned parties. So conflict can be serious problem in any organization. If not handle it carefully or properly it can hurt an organization's performance. Managers therefore have to take appropriate steps in order to manage conflict in a constructive way. So with this background let us now discuss about the positive and negative conflict. Positive attitude towards conflict. It is a conflict that encourages people to solve their differences, to participate in developing an ethical and fair organization and to directly handle injustice. The creation and resolution of conflict can lead to constructive problem solving. The conflict resolution process can stimulate innovations and positive changes as well as make change acceptable. And on the other hand negative attitude towards conflict can have a serious negative effects, diverting attention from the goals and depleting resources then especially time and money and also conflict can negatively affect the psychological well-being of the employees and causes stress. And severe conflicting thoughts, ideas and beliefs can lead to resentment and tension and anxiety in the organization. Now let us discuss some of the types of conflict. So broadly in this video we will discuss about three types of conflict that is personal conflict, group conflict and organizational conflict. All these types of conflict can be further classified in terms of intra or inter. Intra means within and inter means across. So these conflicts are inter related and affects each other in the organization. So first let us discuss about the personal conflict, the interpersonal conflict. So this involves two or more individuals rather than one individual. Two men competing for the same accommodation or two managers competing for the same promotion, two executives steering for a large share of corporate capital are some of the examples of conflict between the individuals and these are quite familiar with us. And the most commonly cited reasons for interpersonal conflict are personality differences, differences in the perception, then clashes of values and interest and power and status differences. Now let us discuss about the intrapersonal conflict. So it is an internal to the person and is probably the most difficult type of conflict to analyze. And intrapersonal conflict is conflict within one person that I have said and a person can be attracted to two equally appealing alternatives. For example, two good jobs, when we get two good jobs offers then there is approach-approach conflict or repelled by two equally unpleasant alternatives such as the threat of being fired if one fails to identify a co-worker's guilty of breaking plant rules. So these are the avoidance avoidance conflicts. So these are some of the intrapersonal conflict and in any case the conflicts is within the individual. Now let us discuss about the inter-group conflict. So conflicts that is between the teams and the groups are termed as inter-group conflicts. They result because of oppositions, disagreement and dispute between the teams. So intra-group conflict includes the disagreement within group members on a certain issue and that leads to ineffectiveness in the group's functioning. By inter-organizational conflict, it means that the conflicts between the organizations are termed inter-organizational conflict. Let us take an example of this form of conflict, maybe the Pepsi-Cola war, then corporate takeovers and mergers, acquisitions can also produce inter-organizational conflicts. Now let us discuss about the intra-organizational conflicts which occurs across departments in an organization, then within work teams or other groups and between individuals. It is widely acknowledged that intra-organizational disputes or conflict can negatively impact an organization in a significant way and this conflict can reduce productivity, harm morale and diminish the stated goals of firing and retaining the best qualified and competent employees. Now let us discuss about the strategies for managing conflict. The five interpersonal conflict handling styles represent various combinations of assertiveness and cooperation. So here in this figure you can see that the Thomas Kilman conflict model has been given and the reflective of a useful two-dimensional model of understanding and comparing the conflict resolutions behavior are depicted here. So this also represents the different combinations of assertiveness and cooperativeness. So let us first discuss about the avoiding or withdrawal style. This enables a person to stay away from conflict, ignore disagreement or remain neutral. This style reflects an aversion to tension and frustrations and may involve a decision to let a conflict work itself out. This strategy is associated with behaviors such as withdrawal, indifferences, then apathy, then flight, then reliance upon fate and isolation. Now let us discuss about the forcing or dominating style. It refers to assertive and uncooperative behavior and represents a win-lose approach to interpersonal conflict and those who use this forcing approach try to attain their own goals without concern of the others. This style includes aspects of coercive power and dominance. It may help a person achieve individual goals but as with the avoiding style forcing tends to result in an unfavorable evaluation by others. So by accommodating and smoothing style, it refers to cooperative and unassertive behavior. Accommodation may represent an unselfish act, a long-term strategy to encourage corporations by others or submission to the wishes of others. Then let us discuss about the collaborating or we can say win-win style. It refers to strong cooperative and assertive behavior and it is the win-win approach to interpersonal conflict handling, a person using collaboration desires to maximize joint results. Then let us now discuss about the compromising or lose-lose style. This refers to the behavior at an intermediate level of cooperation and assertiveness. People using this style engage in a give-and-take strategy and can make a series of concessions and this is a traditional method of resolving conflicts. So dear learners, with this we have come to the end of the first part of the unit Contemporary Issues in Management and in this unit we have discussed about the various aspects of conflict and thank you so much for watching this video.


So, we began to get some feel about the fully vataisan transformations, and essentially the fully vataisan transformations achieve quite a lot, but one thing that I want to draw your attention to is this remark from Bjorken and Drell's book that they help us see different interactions of an electron with the electromagnetic field in a form that we can really recognize, we can interpret easily that is the kind of form that we see in various books. If you read Branstad and Joshen's book physics of atoms and molecules, you will see various terms you know which are referred to as relativistic terms, spin orbit interaction and so on. But those terms are not directly manifest in the Dirac equation and what the fully vataisan transformations help us achieve is to display them in a form that can be very easily interpreted. So, our basic problem is right here that you have the Hamiltonian which contains the odd operators and you want to transfer it to a different representation, transform it into a different representation using this transformation relation that we have discussed. And the objective is to make the transformed Hamiltonian relatively free from the odd operators, we cannot make it completely free from the odd operators, but as much as we can. So, we discussed the first fully vataisan transformations and then you have the leading odd terms which is of the order of 1 over m and then what we are going to do is to have another fully vataisan transformation and now you subject the first transformed Hamiltonian to the second fully vataisan transformation which is S 2 which is through this operator and now you get a transformed Hamiltonian which is H double prime and now you do it one more time following the same procedure. So, we have seen how to work out this algebra, it is a little laborious, it is fun to do and when you do it the third time you get a transformed Hamiltonian which is free from the odd operators to a very satisfactory extent and this is the form you get for the Hamiltonian in the Dirac Hamiltonian in the representation after subjecting the original Hamiltonian to three successive fully vataisan transformations. Now, you know what these operators are theta and epsilon, these are the short forms for the various terms that we introduced earlier and if you look at it you still need to evaluate all these commutators and there are a number of terms to work with and we will suggest to you how these terms are analyzed or at least you know the general trend in the analysis of this. So, that you can work out the details. So, look at this term this is theta square by twice m c square which is appearing here. So, let us see it is explicit form theta is the c alpha dot p minus e over c by a. So, now I am using the Gaussian units which is what I need to use and some of the earlier relations I think were in natural units where I had put c equal to 1 and you know h cross was also set equal to 1. So, here we have placed them and now you have this alpha dot this generalized momentum and then you have the square of it. So, now if you plug in the expression for alpha which is this matrix operator 0 sigma sigma 0 then you get sigma dot pi and sigma dot pi from these terms and you can write this as sigma dot pi sigma dot pi times the unit 4 by 4 matrix. And for sigma dot pi sigma dot pi you can use the poly identity which we have used a number of times as a matter of fact we are going to use it quite often it is something which gets very extensively used. So, this is our explicit expression for this term and we have to analyze this further. So, this is what we get for one of the terms in the transform Hamiltonian. Now, you need the pi cross pi over here which will involve this curl of a operator and a dot del operator, but then we have studied this that this is an operator and this will operate on an operand and we have done this analysis earlier we should always be very careful whenever we have the gradient operator. So, this is not just the magnetic field b, but it is the del cross a operator which would operate on an operand. So, you will end up taking the curl of a product of a and f. So, when you do that then these two terms cancel and you get the magnetic field coming from this. So, that is what we will go here and now you have the magnetic field and that tells you that this theta square over twice m c square operator is this pi square over 2 m and then with this i sigma dot pi cross pi term for which we use this relation we get h cross over c times sigma dot b. So, this is the term which will contribute to the beta theta square over twice m c square in the transform Hamiltonian, but then there are the terms there is this beta theta square over twice m c square and there are plenty of other terms to work with. So, let us have a look at this one this is theta comma e plus i theta dot and we have some indication of how this term is to be used. So, substitute the terms explicitly. So, theta is c times alpha dot the generalized momentum which is p minus e a then this epsilon is e phi. So, all I have done is to substitute these terms and I have a time derivative of the scalar product of these two operators. So, I get d alpha by d t dot pi plus alpha dot d pi by d t, but the rate of change of any operator d omega by d t you get it from the Heisenberg equation of motion. So, you can use that and insert it. So, first of all this term would go away this is not going to contribute anything this commutator would go to 0 then you have this a dot alpha dot gradient term and again we have to remind ourselves that whenever we see the gradient term we have to be careful with that operator because this is the commutator of alpha dot del with phi. So, this commutator is alpha dot del phi minus phi alpha dot del operating on f and if you follow the same reasoning as we did earlier you see that these two terms cancel and you are left with only alpha dot del phi. So, that is what you have got from this commutator. So, from this commutator there are two terms which reduce to a single equivalent operator which is alpha dot del phi and we will use this over here and then simplify this relation for combination of these two terms. So, this is the term we are looking at this alpha dot del comma phi commutator we have simplified and this del phi you know is related to the electric intensity, but there will in the expression for the electric intensity there will also be the rate of change of the vector potential. So, there is a minus 1 over C del a by del t and now you can put in this term in place of this commutator. Now, these are known things these things you know from electrodynamics you know them from elementary vector calculus you know them from quantum mechanics and what you do here is put it all together. So, that is what makes it really interesting. So, put it all together and now you have these terms systematically written as e plus 1 over say del a by del t you see where it is coming from and then you have the d alpha by d t and d phi by d t for these two terms and here you can use the Heisenberg equation of motion and use these to represent these derivatives. So, do not forget that this is an operator. So, which is why you have to use the equation of motion for the operator and now you have got from the equation of motion these terms you have collected all of them and since we have them written on this screen it saves me the time to write all these terms on the board, but this entire file is uploaded at the course web page. So, you can go through it carefully and make sure that you follow the derivation term by term, but here I want to show you in the class and this way we can go much faster than we would if I were to write this on the blackboard, but if you have any difficulty you should stop me. So, this entire file has been uploaded and you have these terms coming from the equation of motion. So, what have we got all the terms have been spelled out explicitly. Now, these commutators again if you make use of the matrix structure and look at the commutation properties you will be able to see that they cancel each other for that you have to work out the matrix operations and there is also a vector algebra which is involved you have to respect the vector algebra, the matrix algebra, the operator algebra everything comes together and by using that these terms will make no contribution these two terms cancel each other they are the same with opposite sign this one with a plus sign and this one with a minus sign. So, these two terms cancel each other and you are left you are led to a lot of simplification and this is what gives you one part of this commutator and that means that you have to get the commutation of theta with alpha dot e. So, here you had so many terms now all of them are replaced by just one commutator is now what you have to determine. So, your task is much easier now and when you do that again do it term by term it simplifies a lot because you get rather familiar expressions over here this alpha dot p alpha dot e this will suggest to you what kind of relations you can use because whenever you see terms of this kind you know that you will be able to use the poly identity. So, it is not that you have to remember what am I going to do next those suggestions are built into the structure of the equation and if you just use them you will be automatically led to do the right thing that is the idea. So, here you see the poly identity merging out of this matrix structure and you get the sigma dot p sigma dot e from this matrix multiplication of these two operators these are matrix operators. So, you have the term here in the first row in the first row of the equation. So, in first column will be the sigma dot p sigma dot e from these two right. So, that is how you get sigma dot p sigma dot e over here and also in the 2 2 position, but each sigma is a 2 by 2 matrix of course. So, you are really working with 4 by 4 matrices which is what you always do in the Dirac formalism. So, you got the sigma dot p sigma dot e and now you can use the poly identity which is which will give you p dot e plus i sigma dot p cross e and you have a similar expression over here, but this time you have got the e cross p. So, these are the 2 terms now let us have a look at this p dot e term p again has a gradient operator. So, you have to be careful with it and what you find from a careful handling of this gradient operator which now we have done a number of times you see that this p dot e will give you this scalar p dot e plus e dot p. So, this is not the same as this, this is an operator this is the result of all the operations carried out. So, now you can put all of these terms back in this expression for 1 over 8 m square c to the 4th and you write all of these terms coming from here and you find that this e dot p term cancels this e dot p, this e dot p is a descendant of this term here this is minus e dot p. So, that is the one which is coming here and these 2 cancel each other now you have this these 3 terms 1 2 and 3. So, these are the 3 terms 1 2 and 3 of which p cross e again with a careful handling of the gradient sitting in the p will give you these 2 terms p cross e minus e cross p we have done this. So, there is a gradient sitting over here. So, using this these 2 terms. So, instead of this p cross e term now you have this p cross e coming from here and then here you have a term in minus of e cross p, but then together with this minus sign it becomes a plus.  Now, you notice that the last 2 terms these 2 terms are exactly the same this is e h cross over 8 m square c square sigma dot e cross p. So, these are the same term. So, instead of the 1 over 8 factor you will have the 1 over 4 because you can combine those 2 terms. So, that is what you have got you get the 1 over 4 here coming from these 2 terms and then from here you get this sigma dot curl of e and now you are perhaps beginning to see some familiarity with some of the terms you may have seen in perturbation theory, but they will become even more explicitly manifest after just a few more steps. So, this is what we have got these are the 3 terms. So, you get a divergence of e you get sigma dot curl of e and a sigma dot e cross p. So, let us write insert them in the transform Hamiltonian. Now, when you take care of all the terms and put them back into the transform Hamiltonian which is the transform Hamiltonian arrived at after 3 full d vitties and transformations. The transform Hamiltonian then has got so many terms 1, 2, 3 and then you have got another 1 over here and all of these terms are now amenable to easy interpretation rather easy interpretation. This was not the form in which we could see them in the Dirac Hamiltonian they were there it is not anything that we have added ad hoc. This is come straight out of Dirac Hamiltonian by subjecting it to appropriate transformations you immediately see that this electric intensity is nothing but the gradient of the potential and this e r is this position vector divided by r. So, you see the form minus 1 over r del v by del r and now you have got this r which will come here.  It comes so nicely out of the full d vitties and transformations it was there in the Dirac equation but it was not visible and when you subject the full d vitties and transformations to 1, 2, 3 transformations then in the third result which is the h triple prime you see this form appearing. So, this is the e h cross p.  Now, this is the relativistic kinetic energy which is e minus m c square and you remember we defined the energy mass equivalence very carefully at the very beginning without which we would not have this connection. So, there was a strong reason to spend some time discussing that and you will see that it is important. So, the relativistic kinetic energy is this difference which is the energy minus the rest mass energy what you take away after removing the rest energy is the kinetic part. So, that is the relativistic kinetic energy and now all you do is to expand this term to the power half and when you do that you get a power series and you have got c in the denominator whose powers keep increasing. So, you can truncate it at some level of approximation wherever you want and if you keep the leading term the most important contribution comes from the p to the 4 term. So, this is the relativistic kinetic energy term this is precisely the term that we saw in the foldivotison transformed Hamiltonian. So, there was a term in p to the 4 and we see its origin in the fact that the relativistic kinetic energy is different from the Galilean kinetic energy the two are different. So, its origins can be traced the origin of the p to the 4 term which is here this can be traced to the relativistic kinetic energy part this is what we just saw. This sigma dot b is a magnetic dipole moment term as is easily recognizable then you have got a term in the divergence of e and this was introduced in the pre foldivotison days as a perturbation and it was referred to as the Darwin correction. So, in some books on perturbation theory they will begin with a non relativistic Hamiltonian and add perturbations that this is the perturbation due to the relativistic kinetic energy because your original Hamiltonian is not relativistic let us take into account some of the relativistic features. And let us do it perturbatively because after all the non relativistic theory is not absurd it gives a good starting point it certainly does at the reason of course, is that the speed of light is extremely high even if finite it is extremely high. So, the non relativistic Schrodinger equation non relativistic quantum mechanics is not absurd, but not quite accurate. And we are now looking at those effects which are really important because an atomic spectroscopy and atomic processes it does become important to take into account relativistic effects and not just for heavy atoms, but even for very small atoms even for the hydrogen atom. It is absolutely important to take these effects into account and these could be introduced perturbatively in non relativistic mechanics. So, you can add the kinetic energy correction as a perturbation you can add this is the correction you can add the spin orbit correction actually these two terms together contribute to the spin orbit term rather than just the last one. The last one is more famous because curl of e for the hydrogen atom vanishes that is spherical symmetric potential. So, you know the curl of e vanishes. So, this one is not of important, but if you are dealing with the potential which is not strictly central field then you are going to have to take this into account and you cannot throw it away. So, relativistic quantum mechanics will give you not just the sigma dot l term not just the s dot l term, but an additional term which must be taken into account as an integral part of the spin orbit interaction that is a relativistic effect for a central field it is just the sigma dot l and of course, there is this d v by d r and so on. So, there are these terms and one can make corrections perturbatively and it is a good idea to see the correspondence. So, let us look at the perturbative correction due to the kinetic energy part this is the relativistic kinetic energy correction coming from the p to the 4 term. Now, you see that this is the square of p square and this is e n minus v whole square and you really need the expectation values of the potential energy and also the square of the potential energy. So, you need the average values of 1 over r because the potential energy goes as 1 over r and you also need the average energy of 1 over r square. Now, these problems you would have done in non relativistic hydrogen atom how to get the average expectation value of any operator. So, if you take the n th wave function for the hydrogen atom and determine the average values of 1 over r and 1 over r square you will see that 1 over r goes as 1 over n square 1 over r square goes as 1 over n cube a is a more constant and then there are other constants other quantum numbers which come in. So, you can use these relations put them in the expression for the average energy for the potential energy and the square of the potential energy and that will give you an estimate of the perturbative correction due to the relativistic kinetic energy and it turns out to go as alpha square where alpha is the fine structure constant. This is the reason it is called as a fine structure constant because it changes this non relativistic structure even if so in only a fine small detail and it contributes some details to the atomic structure. So, this is the fine structure constant, but this is not the only term which is coming because of relativity and this is the most important lesson from the Foldy-Vortaisan transformations because if you do perturbative corrections to non relativistic Hamiltonian, then which are the corrections you have to make means you could make the Darwin correction you could make this correction you could make this correction. So, there are three corrections that you can talk about and perturbatively you might say that this is the most important one I will do that I could do the second term or I could do the third term or I could do the second and the third, but not the first, but whenever you are making corrections it is extremely important that if you include one term of a given order then you consider all terms of the same order and you are certainly making an approximation. So, it is not an exact formalism that you are developing anyway whether it is the Foldy-Vortaisan scheme of doing things or the perturbative way of doing things you are not doing an exact analysis you are making approximations. So, make sure that your approximation is sensible because you when you make an approximation and say that argue that these terms I am not going to take into account because they are weak they are ignorable nothing wrong in making that argument, but you cannot ignore those terms which are of the same order as some of the other terms you have chosen to include. So, you have to take into account all of them and when you do not do that you will obviously, get wrong results. So, now this is the correction due to the relativistic kinetic energy and now let us see the correction due to the spin orbit term which is the sigma dot l term over here and here again you can go ahead and determine the expectation value of this operator this is the first order perturbation theory result which is quite familiar to you. So, you need the radial integral for 1 over r cube because del v by del r will give you the derivative of 1 over r which goes as 1 over r square. So, you need the expectation value of 1 over r cube because of that reason and then you get you need the expectation value of this operator in angular momentum states.   So, you have a twice s dot l terms. So, you will get h cross square by 2 j into j plus 1 minus l into l plus 1 minus s into s plus 1 and then the average value of 1 over r cube will give you this term in 1 over n cube and some of the other quantum numbers is including the orbital angular quantum number. So, this is the correction to the energy because of the spin orbit term and it is as important as the relativistic kinetic energy term which is sometimes referred to as the relativistic mass term, but more appropriately it should be called as the relativistic kinetic energy term because we do not make a distinction between mass and energy that something that we have already taken care of. So, you can simplify this expression for the average value of the spin orbit interaction. These are the constants that you make use of the Bohr radius and the fine structure constant and you find that this is the same as what is some books call it as relativistic mass correction, but it is a relativistic kinetic energy correction as I prefer to call. So, this is what you get the spin orbit correction again goes as z alpha square. Now, this is the correction from relativistic kinetic energy which goes as z alpha square and now you are left with one more term because here is a simplification of this further the spin orbit interaction of course, is important only for l not equal to 0 states because for l equal to 0 the l plus s and l minus s will give you the same thing. So, this is when l is not equal to 0 you can explicitly put in the values and find these simplified expressions for the spin orbit splitting. What about the divergence term? This is the Darwin correction. Now, the Darwin correction requires you to take the divergence of e which is the divergence of 1 over r square which gives you a delta function. The divergence of 1 over r square gives you a Dirac delta and you will therefore, need the average value or the expectation value involving this delta function. So, when you evolve when you determine the expectation value of the operators you must use the delta function integration expectation value is an integral obviously. So, this is let us say you take the expectation value for some n s state this is important for l equal to 0. So, this is let us say for some non relativistic wave function psi n with l equal to 0 and m equal to 0 and you determine this integral and this will give you minus e n z alpha square over n. So, again you find that the Darwin correction is also of the same order of magnitude as the other two. So, it is important to take into account all the three if you want to make relativistic corrections at all or none at all. If you do only one or the other then it is not enough and that is the difficulty with perturbative approach to quantum mechanics. Because whenever you try to make improvisation and add terms which you even if they are in the right direction they can still give you completely wrong answer because you may have two contributors of the same order of magnitude. They could come with opposite signs and they could just kill each other or they could come with the same sign they can they could add to each other. So, these are various factors that you have to consider when you do perturbation theory. So, this of course is important only for l equal to 0 because it requires a finite amplitude of the wave function at the nucleus at r equal to 0. And you know that all the radial functions of the hydrogen atom they go as r to the power l as r goes to 0. So, as r goes to 0 the wave function goes as r to the power l and for l equal to 0 this will be finite at the origin at r equal to 0. But for l equal to 1, 2, 3 and everything else this would go to 0 and it would go to 0 faster for higher values of l which is a centrifugal barrier effect which I had discussed in unit 1 I believe. But this is of importance for the n s state. So, this is for the l equal to 0 state that this is important. And then you have these three corrections the relativistic kinetic energy the spin orbit correction the Darwin correction they are all of the same order z alpha square. And you therefore put them all together and add the net effect of these three terms to the correction. And these three terms when you add together you get a net relativistic correction for all orbital angular momentum quantum numbers. And this is the result that you get from relativistic quantum mechanics. But if you did not use all the three but only one or this this is not what you are going to get. So, please make a very major note of this point that all perturbations of the same importance must be included together. So, now our primary intention in doing this exercise was to solve the Dirac equation for the hydrogen atom. Now, we have seen what some of the terms mean and these are some of the references that I like very much for this topic Bjorken and Greiner and Triggs quantum mechanics messiah. So, these are some of the books that I have used and for the coulomb problem for the hydrogen atom you can solve the Dirac equation exactly. In all the forms that we used until now we had the potential v of r but we never actually specified it to be the coulomb potential. So, for the coulomb potential Dirac equation has got an exact analytical solution. So, now let us see how we are going to handle this and it is not at all trivial. The reason to discuss it is because it is not a trivial extension of the non relativistic methods. In non relativistic quantum mechanics you varies in a very simple manner you separate the radial part from the angular part because of the 1 over r potential. Now, that is not so obvious for the Dirac case because of the presence of the odd operators and if you look at the Dirac equation now. In fact, if you look at the Dirac equation even for a free particle let alone a particle in an electromagnetic field. So, even if you throw the terms in A and phi you find that the orbital angular momentum operator and the spin angular momentum operators do not commute with the Dirac Hamiltonian even for a free particle. And then of course, they will not commute for the Dirac Hamiltonian for the coulomb problem because those terms are also there. So, it is not going to commute which means that these will not give you good quantum numbers because our whole idea of good quantum numbers is to get them from those operators which commute with the Hamiltonian. So, that they correspond to simultaneous compatible observations. So, what constitute compatible observations to give you good quantum numbers is a question and we have to get the good quantum numbers for the Dirac Hamiltonian and it is not going to be n l m. L cannot be a good quantum number because l does not commute with the Hamiltonian. So, your quantum numbers are going to be different because of the spin orbit interaction, the spin orbit coupling and then parity also has to be defined in a very careful manner for the Dirac case because of the beta operator which is what is that 1 0 0 minus 1. So, you have to be careful with parity as well. So, this is our spherical symmetry Dirac Hamiltonian and now we want to exploit this spherical symmetry. So, somehow we want to separate the equation into a radial part and angular part and we have to extract angular features and radial features. We have to identify them separately and the main question is how are you going to handle this term this alpha dot p. So, let us discuss this. So, these are our operators I define two new operators. So, this operator which is got 1 in the off diagonal position is what I call as rho 1 I will use it alpha we have already used which is the Dirac operator 0 sigma sigma 0 and this is sometimes called as the Dirac spin. This is made up of the poly spin this is sigma sigma along the diagonal along the off diagonal is the Dirac alpha along the diagonal it is the sigma into the unit matrix operator or this is sometimes written with a sigma with a superscript d for Dirac or sometimes with this uppercase sigma. So, these are the various notations that you see sometimes it is written only as this sigma which is the same as the poly sigma, but from the context you know whether it is the poly sigma or the Dirac sigma. If it is the Dirac sigma it is a 4 by 4 vector operator likewise the spin angular momentum which is h cross over 2 sigma is now you extend this idea to the 4 by 4 operators and this is h cross over 2 this uppercase sigma. So, this is the notation I will be using. So, this is h cross over 2 sigma and you have got a unit operator you can also write this as h cross over 2 sigma or you can just not write this one operator in which case you will read it as just the usual poly h cross over 2 sigma, but from the context you should know what you are talking about. So, notice this rho 1 sigma is the same as alpha rho 1 alpha is the same as sigma and if you look at sigma dot p you can extract the sigma dot p and you have a unit operator. So, sometimes you will find books in which this sigma dot p is written only as this sigma dot p, but they are the same things they are the same yet different one has got a 4 by 4 structure and the other has got a 2 by 2 structure. So, which is why one is the poly sigma the other is the Dirac sigma, but you have to be careful while reading literature because many books do not alert you to this although I am sure that they would have said that somewhere, but you have to read it very carefully. So, this is sigma dot p now I have got sigma dot p here as well. So, obviously the rest of it over here is the unit operator which you can easily recognize because this is the projection of sigma in some direction because this r over r is the unit operator I do it twice and sigma square along any direction is equal to 1. So, this is just the unit operator. Everybody is comfortable this is just the projection of sigma on some direction sigma dot u and what is the square of sigma dot u it is like sigma z square it is equal to 1. Now, everybody will agree it is right indeed it is. So, it is just like sigma z square which is equal to 1. So, that is what you have got and now here you make use of the poly identity. So, this is r dot p plus i sigma dot r cross p here you would expect a 4 by 4 unit matrix sitting implicitly. So, this is sigma dot r this is r over r square. So, this is e r over r this is the unit vector in the direction of the position vector and this r dot p gives you if you represent the gradient operator in the spherical polar coordinate system you will need to work with only one of the components which is this and you know that the radial momentum operator is not just minus i h cross del by del r it is minus i h cross del by del r minus i h cross over r. So, be careful about it because you have to put that in the expression for r dot p which is minus i h cross r del by del r which is r p r plus i h cross. So, you have this extra term.  So, you can put that over here you have got a sigma dot l coming from here. So, you put all the terms together and you have essentially sigma dot e r, but then our interest is in alpha dot p and what is alpha it is rho 1 sigma and rho 1 is this operator this matrix which has got 0 1 1 0 with the elements 1 in the off diagonal position. So, when you pre multiply sigma by rho 1 you get the alpha.  Now, p r I have written explicitly in terms of this minus i h cross del over del r minus i h cross over r and now this term and this term will cancel. Now, this term now you see on the right side you have got expressions involving radial character and this is what we set out to do because our Dirac Hamiltonian for the spherical potential is the c alpha dot p plus beta m c square plus v and now we have succeeded in writing alpha dot p with radial features. It is not completely separated into radial and angular part and you will see that in the next class, but you are beginning to see that you are now able to see the radial features which is what you need to separate the radial part from the angular part and to be able to do the analysis completely we are going to introduce a new operator which is defined as k which is this h cross plus sigma dot l h cross plus sigma dot l why is this so important it is coming here h cross plus sigma dot l. This is the one which we think could create some trouble for us this is the operator which needs to be carefully handled. So, we in fact define a new operator which is beta k which is equal to h cross plus sigma dot l. So, that makes k itself go as beta h cross plus sigma dot l beta square is equal to 1 we know that. So, this is a new operator that we introduce and now in terms of this new operator your alpha dot p operator becomes alpha r p r plus i over r beta k where k is this new operator that we have defined. We can rewrite the Dirac Hamiltonian in this form in terms of this new operator and if you collect all of these terms together you have got the Dirac Hamiltonian for the spherical potential in terms of the k operator and this is where I will stop today and take this up from here in the next class. So, we need one more class to see how you actually work out the separation between the radial and the angular part and then see how you get the solutions to the Dirac equation the Coulomb functions and then use them in your relativistic applications. So, thank you very much.


Thank you. It concludes the debate on Scotland's population meeting our political foster Regina of our community's economy about public services. It's now time to move on to the next item of business, which is an urgent question. I call Graeme Simソgdyn. Thank you to ask the Scottish Government what its response is to the claim in the BBC report today that the process for awarding the contract for ferries 801 and 802 maen nhw'n chi'n ei dweud. The allegations by the BBC were first put to me in advance of an interview that I conducted last week as a part of the programme to be broadcast this evening. The Scottish ministers are not aware of any impropriety in the procurement process, but take the claims made extremely seriously. It is important that they are carefully addressed. As I made clear in my interview, those issues are concerning. I know that the current y f liqu kuсти gyda'r Cyfath am Fongol. It has committed that ministers would explore what further steps the Government needs to take to ensure that all the questions about the fairness and appropriateness of the tendering process are properly independently investigated. I can confirm that the permanent secretary at the request of ministers has already pro actively been in contact with the Auditor General to discuss that matter. The Auditor General informed the permanent secretary that Audit Scotland will be looking at the substance the allegations raised around procurement by the programme before deciding if further audit work is required. I welcome this. Scottish Government, CML and Ferguson's all commit to fully supporting that exercise. Graham Simpson. Can I thank the Deputy First Minister for that answer? We found out today that the disastrous Ferries contract does appear to have been rigged in Ferguson's favour. The new documents appear to show that Ferguson's received a 424-page report to help their bid. Nobody else did. Ferguson's was allowed to change its design at the halfway mark nobody else was, Ferguson's was able to change its price after the deadline nobody else could, Ferguson's received a confidential yn llawer o heddiw ddechrau i bwysig oherwydd dyma. Fy meddwl, mae Ffyrguson bydd glik a unigol ar y gwirion iawn. Rwyf wedi ôl amddangos iawn. A oedd gwybodiaeth'r gwirion iawn oherwydd amddangos iawn, oedd yr sgandl yn ysgandl iawn, a dweud i'n gwybodiaeth'u grwpun wedi'i gwirion iawn. Rydym ni'n cael ei wneud yma y gallai hefydau i'n gwybodiaeth hwnnw, mae'n hiwgaf yn ysgandlu. Dwyhaid am gweithio i amddangos, y Debiton y Acroedden ni wefwyd eich ddau i'r newid. Ydych yn ddadill hwn. Mae'r ddaf i'r ddim yn gondol i'r ddestuniau gyda'r perfforddol yn yma i ddim yn ymgwedol yn y BBC News, ac yn ddiddordeb angen i'r ddiddorol, ac yn y newid i'r dsinharau am I have indicated that there are issues of concern that are required to be explored and I welcome the comments made by the Auditor General this afternoon that he is to consider what further audit work is required in the light of the points raised by the BBC report. There are issues of concern, because I do not believe that it would be appropriate for the level of specific information that the BBC documentary believes was available to Ferguson's to have been available to them. It is important that I place on the parliamentary record that CMAL has made clear to the BBC that they can find no trace of that document going from CMAL to Ferguson's. It is important that those points of factual accuracy are put on the record. In relation to the wider questions that are raised, that is why I gave the commitment that those new points of detail and information that have been raised by the BBC documentary need to be explored further. I welcome what the Auditor General has said in that respect today. Graham Simpson. It is no use, the Deputy First Minister, hiding behind the Auditor General. These claims were put to him last week. I cannot believe that he has just been sitting there doing nothing, not finding out what has gone on. So, if the Government accepts this is wrong and they appear to do that, they don't know how it's happened or who's responsible, then surely they must now call in the police to investigate. Because if Ferguson receives special treatment for whatever reason, it's beyond the scandal, it's a crime in my view. This alleged rigging of the contract and its potential fraud has cost the country £250 million and it's rising. So will the Government now call in the police so that we can finally find out the truth of what has happened? Mr Simpson asks what I've been doing since those points were put to me. What I've been doing is asking the permanent secretary of the Scottish Government to raise with Audit Scotland the issues that have been put to us to enable Audit Scotland to consider who, of course, have undertaken audit work already in relation to the Ferguson's procurement process to establish any further inquiry that is required to be undertaken. What that would enable is independent scrutiny of the procurement process to be undertaken, as Audit Scotland do on countless other issues and have done on the Ferguson's contract already. That is what I've been doing because I thought Parliament would want there to be a process of independent assessment of these issues which can be properly considered and any appropriate action taken as a consequence. The reports from the BBC today regarding historic allegations of potential and propriety between Seymal and Ferguson's during the procurement process are clearly concerning. Will the Deputy First Minister provide assurances about the timescale involved in the full investigation of this matter? Obviously, we do not want matters of this nature taking an inordinate amount of time to be investigated. If there are concerns raised, they should be properly looked into. That is the steps that the permanent secretary has taken on ministers behalf in raising this issue with Audit Scotland. I welcome, as I say, what the Auditor General has said this afternoon to enable us to undertake or for there to be independent investigation of the claims that have been made to determine what further action is required to be taken. Rhoda Grant, what is being trailed by the BBC is very worrying, as is the Deputy First Minister's answer about being unable to find any exchange of documents. The Auditor General struggled to investigate the procurement process previously. What changes has he made and what information will he make available to allow the Auditor General to investigate thoroughly? In the interests of full transparency, will he now agree to an independent public inquiry into the whole fiasco and, indeed, to call in the police if corruption is suspected? In relation to the point that Rhoda Grant puts to me in connection with any further investigation, I have set out to Parliament the steps that we have taken to enable there to be what were to raise with Audit Scotland the issues that have been put to us and Audit Scotland have made their own judgment as they should do as the independent auditing body within Scotland. In relation to documentation, I remind Rhoda Grant that the Government published a huge volume of material in December 2019, if my memory serves me correctly, which went through all of the detail around the information that was available on the procurement process and the development of the contract with Ferguson's. As I have indicated in my answer today, the Scottish Government, CMAL and Ferguson's all commit to fully supporting any investigation that is properly undertaken under the auspices of the Auditor General. We were told by ministers that everything was out in the open and that the Government had nothing to hide, so why is it that we are only finding out about this now and what does it say about the oversight function within the Scottish Government? As I set out in my answer to Rhoda Grant, the Government published a huge volume of material in 2019, which covered all aspects of the procurement process. Obviously, there are specific points raised with us about the information to which Ferguson's had access, which was information that ministers did not previously know was the case. That is why we have taken the steps that we have taken in raising these issues with Audit Scotland today, to enable Audit Scotland to be able to make a judgment about the issues that are raised in the BBC documentary. The Government wants to make sure that any question that is raised in that respect is properly and fully considered as part of the analysis that should properly be undertaken on the awarding of a contract, if concerns of this type are raised. Thank you. That concludes the urgent question. There are three questions to be put as a point of order, Douglas Ross. I wonder if you could outline to those of us who represent Murray and the Highlands how we could encourage the Scottish Government to provide a statement or, hopefully, a full debate on the future of maternity services in Murray. You will be aware, Presiding Officer, that SMP members are saying to raise it. We will hear Mr Ross. We have the public health minister laughing that this is not a point of order. I really hope that she comes back with more than laughter, because no-one in Murray and no-one in the Highlands and Islands is laughing about this issue. I am sure that all members of this Parliament are firmly committed to the idea that all voices are heard in this chamber, but I would prefer to hear one voice at a time. If we could hear Mr Ross, thank you. I am grateful, Presiding Officer, because you will be aware that the Scottish Conservatives proposed at the Bureau this morning that the Scottish Government do dedicate time this week to debate this issue. This follows an amendment to the business that I tried to make on 28 June this year, because we know that NHS Grampian announced their plans for model 4 on 1 July. At the time, the business minister, Mr Adam, assured us that there would be opportunities for this Parliament to debate and scrutinise plans for model 4. Indeed, the health secretary said to the BBC at the time, I intend updating the Scottish Parliament as soon as it is practical at the beginning of the next session. We are now just a couple of weeks away from the end of this session, and the Scottish Government confirmed this morning that they would not include time this week to discuss this issue. It continues to cause great concern for mothers to be and families in Murray, but today NHS Highland looked at the proposal to transfer more Murray women through to Rhaigmoor and to give birth in Inverness, and keep mum, the group who have campaigned so hard for the restoration of maternity services in Murray, called that meeting tone deaf. They said what they heard at the meeting of NHS Highland does not encourage them that anything is going to happen any time soon. Can you advise us how we can get some statements, some answers, some response from the Scottish Government on this issue? Please remember to the SNP members who do not want this to be debated. We were promised over four years ago that the downgrading of maternity services in Murray would be temporary for a year. It is now more than four years later. We need answers, we need a response, we need to hear from the SNP Scottish Government what they are going to do to ensure that we can get maternity services back at Dr Gray's to deliver for the women and families of Murray. Thank you, Mr Ross. For advance notice, it is the case that whether a ministerial statement is to be proposed is a matter for the Scottish Government, rather than a point of order for me to rule on. However, your comments are now on the record. I am minded at this point that there are three questions to be put as a result of today's business, but I am minded to accept a motion without notice under rule 11.2.4 of standing orders to bring decision time forward to now. Minister, the question is that decision time be brought forward to now. Are we all agreed? We are agreed. The first question is that amendment 6063.3 in the name of Donald Cameron, which seeks to amend motion 6063 in the name of Angus Robertson on Scotland's population, meeting the needs of our communities, economy and public services, be agreed. Are we all agreed? No. The Parliament is not agreed, therefore we will move to a vote and there will be a short suspension to allow members to access the digital voting system.


Feelings, in general, are not easy to understand. What's worse, or better, is that we are specifically made to feel something, depending on the situation. Now, every existing thing has two sides of the same coin. This principle is also applied to our emotions, no matter if they are considered good or bad. Today, we'll see more in detail one feeling in particular, envy. Let's take a look. How come you became that interested in a complex emotion such as envy? Many people talk about it, but only a few did a huge research like yours. What motivated you to focus on this specifically? Lately, I've been doing a lot of reading and the literature on communications and relationships. That's when I came across new research on envy.  Like most psychologists, I've just assumed that envy is bad and should be controlled as much as possible. But after looking deeper into it, I've found that it can have a positive side as well. In hindsight, it makes sense human emotions are complicated and they're rarely all good or bad. Everyone has their own Brent in a moment of life or another. It's known that he or she did nothing wrong, that they got what we first wanted for having more skill. Then why do we still get angry at this person? What drives us to make negative thoughts other than envy, anger and frustration? Brent is the character in my article that gets the promotion you wanted. This made up example gives us the opportunity to explore the nature of envy. First of all, we need to think about what emotions are and what they're for. Emotions provide us with information about our current situation and the motivation to do something. Envy provides us with the information about our status and the social structure. Before, you and Brent were equals, but now, for some reason, he's above you. That's what triggers the feeling of envy. After that, it motivates us to do something to mitigate this loss in social standing. Here's why envy can be either positive or negative. It's positive when it motivates us to learn from Brent's example or improve ourselves. In this sense, anytime you look up to a role model, you're experiencing positive envy. But of course, envy can also motivate us to do negative things like spreading false rumors behind Brent's back or trying to sabotage his efforts to succeed. Of course, negative envy doesn't do anyone any good. It doesn't help you improve, and because it disrupts the social network, it can cause harm to other people besides the one you intend to hurt. My guess is that your tendency towards positive or negative envy is probably based on the way you've seen others behave in similar situations, especially when you were young. Would it be possible to just use the bright side of envy to become a better person? Could it also be completely negative one day or another, leading our minds into a vicious cycle in which we can't get out? Now here's where mindfulness comes in. You may have a habit of feeling negative envy anytime someone gets something you want it, but if you're aware of your habits, you can change them. This is especially true when you understand you can turn your negative envy into a positive motivation to improve yourself, and you're right. If we give in to negative envy, it draws us into a vicious cycle that can be hard to escape.  They're not happy people, and they definitely are not pleasant to be around. Is there a way to totally repress our envy in general? Supposing that, could it be cowardly or a wise thing to do if we had the chance? It's never wise to repress your emotions. Like whack-a-mole, if you push down an emotion at one time, it just pops up again at another time, often in an even worse situation. Emotions provide you with valuable information and motivation, so you should never disregard them. Of course, that doesn't mean you should be a slave to your passions, either. You've also got to do a reality check. Use emotion and reason and tandem to guide your behavior. The next time you feel a twinge of envy, embrace the emotion and ask yourself how you can use it to improve yourself. Janling your envy into self-improvement is definitely a wise course of action. Does it boost our hidden capacities that we first didn't think to possess? Is it a great advantage to be envious in this case? That's the whole idea behind positive envy. You can use the feeling to push yourself forward, make yourself better than you were. You can learn from those you feel envious of, but only if you can avoid the dark side of envy. In your article, you correctly said religious leaders and psychologists always view it as a bad thing. Do you think they were wrong or right in some way? Should envy be considered something to avoid or fully embrace, both the dark and bright side? When people say envy is a bad thing, they're talking about negative envy.  However, we should embrace positive envy because of the way it can motivate us to do better. Envy, like all emotions, provides us with motivation to do something, but we can use our reason to channel our envy into a positive course, giving us the motivation we need to improve ourselves. As you stated before, anger and fear are not, of course, the same emotion. Let's just put the case that we feel an emotion considered good. Joy, does it have a negative side too, like every other feeling mentioned before? You make an excellent point. We can see positive and negative sides to all emotion. Fear protects us from harm, but it can also keep us from pursuing opportunities. Likewise, anger can motivate us to protect ourselves when threatened, but when it's expressed inappropriately, it can seriously damage our social relationships. But what about joy, which seems purely positive, or is it? There's no word for the concept of negative joy in English, but the Germans have a good word for it. They call it Schadenfreude, or a shadow joy. You can experience Schadenfreude when you feel happiness at seeing someone else fail or suffer. Slaps to comedy is based on Schadenfreude. You laugh when the comic slips on a banana peel, gets hit on the head, or falls into a manhole. I suppose we're thinking, good thing that's not happening to me, but of course we know that's just an act and nobody is really getting hurt. But we can also relish the real pain of other people, and let's say you've been stewing over Brent stealing your promotion, and now you learn he just got fired. Schadenfreude. But still, what good does it do to you? Like negative envy, it's corrosive to yourself as well as everyone else in your social network. So I suggest we keep on the bright side and avoid the shadowy aspects of all our emotions. When was a time you felt envious of another person? Was it positive or negative envy? Feel free to share your stories in the comments below. If you enjoyed this video, be sure to check out our website and other social media, as well as our new Patreon account. And don't forget to subscribe. Thanks for watching.