Square-Well Potential by an Algebraic Approach

摘要

This paper provides an algebraic approach to the celebrated quantum-mechanical problem of a particle in a box. There are two primary reasons for such a formulation. The first is that the potential and therefore the spectrum are quite anharmonic. Hence simpler algebraic techniques were the Hamiltonian is one of the group generators, which lead to, at best, a quasiharmonic spectrum, will just not work for this potential. Systematic methods are, in principle, available for handling anharmonic systems. Also, model algebraic Hamiltonians which are bilinear in the generators have recently been extensively employed in both nuclear and molecular physics. It is therefore of interest to see whether these techniques will work for this benchmark problem.