Calculation of energy eigenvalues via supersymmetric quantum mechanics

Abstract

A systematic procedure using supersymmetric quantum mechanics is presented for calculating the energy eigenvalues of the Schrödinger equation. Starting from the Hamiltonian for a given potential-energy function, a sequence of supersymmetric partners is derived such that the ground-state energy of the kth one corresponds to the kth eigen energy of the original potential. Various theoretical procedures for obtaining ground-state energies, including a method involving a rational-function approximation for the solution of the Ricatti equation that is outlined in the present paper, can then be applied. Illustrative numerical results for two one-dimensional parity-invariant model potentials are given, and the results of the present procedure are compared with those obtainable via other methods. Generalizations of the method for arbitrary power-law potentials and for radial problems are discussed briefly.