An analytic iterative approach to solving the time‐independent Schrödinger equation

Abstract

ABSTRACT:In this article, we introduce a simple analytic method for obtaining approximate solutions of the Schrö dinger equation for a wide range of potentials in one-and two-dimensions. We define an operator, called the iteration operator, which will be used to solve for the lowest order state(s) of a system. The method is simple in that it does not require the computation of any integrals in order to obtain a solution. We use this method on several potentials which are well understood or even exactly solvable in order to demonstrate the strengths and weaknesses of this method.