Local behavior in supersymmetric quantum mechanics

Abstract

In supersymmetric quantum mechanics, the differential equations corresponding to exactly solvable potentials may be treated by algebraic methods. By use of a system of geodesic polar coordinates on a Riemannian manifold, and subsequent transformation to a Schrödinger equation with a potential in two ways, it is demonstrated that the local behavior of the exactly solvable potentials considered in supersymmetric quantum mechanics corresponds to isotropic harmonic oscillator and Pöschl–Teller potential problems.