Convergent Iterative Solutions of Schroedinger Equation for a Generalized Double Well Potential

TL;DR

This paper introduces a convergent iterative method to solve the Schrödinger equation for a generalized double well potential, analyzing ground state properties and convergence conditions.

Contribution

It provides a new explicit iterative approach for the lowest energy state in a complex double well potential, including convergence analysis and wave function shape dependence.

Findings

Convergent iterative solution for the ground state energy.

Dependence of wave function shape on parameter a.

Conditions for convergence of the iterative method.

Abstract

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with a generalized double well potential $V=\frac{g^2}{2}(x^2-1)^2(x^2+a)$. The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameter $a$ are discussed.