Application of the asymptotic Taylor expansion method to bistable potentials

TL;DR

This paper applies the Asymptotic Taylor expansion method to solve the Schrödinger equation for bistable potentials, providing analytical eigenfunctions and accurate eigenvalues with a simple computational algorithm.

Contribution

The paper introduces the use of ATEM for bistable potentials, offering a straightforward algorithm for analytical and numerical solutions of the Schrödinger equation.

Findings

ATEM yields eigenfunctions with optimal truncation.

Eigenvalues obtained are highly accurate and consistent with existing literature.

The method is easily implementable using symbolic or numerical computation.

Abstract

A recent method called Asymptotic Taylor expansion (ATEM) is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrodinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical result for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results appropriate with the existing literature.