Quasi-algebraic treatment of bound states of simple one-electron systems

摘要

We present a straightforward, quasi-algebraic treatment of simple one-particle quantum-mechanical systems. The method consists primarily of a canonical transformation that changes the Schrödinger equation into a first-order differential equation, thus allowing an easier derivation of the eigenvalues and eigenfunctions. We express the latter in a way which is not commonly encountered in the standard literature on quantum mechanics and quantum chemistry. The derivation of generating functions for the eigenfunctions offers no difficulty because the method is formulated in the coordinate representation. As illustrative examples, we consider the harmonic oscillator and a particle in a Kratzer potential