This technique is used in quantum mechanics to show that the expectation value of the Hamiltonian in any normalized state is at least as large as the ground state energy.
V.I. Arnold used this technique to demonstrate that the energy functional is the same for the set of all flows isovortical to a given steady flow. This technique can be used in approximate solutions to the Boltzmann equation by showing that the correct solution is one for which a certain integral expression involving that solution is bounded above by zero. Another use of this method in statistical mechanics is to show that the condition of maximum probability is equivalent to the condition of maximum entropy. This technique is used in quantum mechanics to show that the expectation value of the Hamiltonian in any normalized state is at least as large as the ground state energy. This technique is also used to show that for the "correct," trajectory, the time-integral of the Lagrangian, or the action, is stationary by slightly changing the action from the "true" path. Used in the derivation of Fermat's principle of least time, for 10 points, identify this mathematical technique of finding a function which extremizes some variables.
V.I. Arnold used this technique to demonstrate that the energy functional is the same for the set of all flows isovortical to a given steady flow.
variational method or principle or calculus