Saint Louis University

For many years Dr. Santhanam has been studying one of the root concepts of Quantum Mechanics - the so-called "commutation rules". These form the basis of the well-known Uncertainty Principle of Quantum Mechanics, which specifies which physical quantities - such as position, momentum, energy, etc. - can be measured simultaneously, and which ones cannot. These commutation rules not only depend on the specific physical quantities, but also on the type of physical system that is being studied, i.e. individual atoms & particles, group of atoms, etc. Most importantly, they also depend on the type of energy spectrum that they have. Dr. Santhanam's interest has been on finding out those commutation rules that apply to systems possessing only a finite number of energy levels (in contrast to those systems that have a infinite number of levels, like ordinary atoms). With collaborators he has come up with the relationships shown below,which have attracted the attention of theoretical physicists from around the World.

SLU Physics