Calculation of the eigenfunctions and eigenvalues of Schr\"odinger type equations by asymptotic Taylor expansion method (ATEM)

TL;DR

This paper introduces the asymptotic Taylor expansion method (ATEM) for analytically approximating eigenfunctions and numerically computing eigenvalues of Schrödinger-type equations, optimizing the Taylor series truncation for best results.

Contribution

The paper presents a new asymptotic Taylor expansion method (ATEM) for solving Schrödinger equations, providing analytical eigenfunctions and accurate eigenvalues through optimal series truncation.

Findings

Effective analytical eigenfunctions derived

Accurate numerical eigenvalues obtained

Method applicable to various Schrödinger problems

Abstract

A novel method is proposed to determine an analytical expression for eigenfunctions and numerical result for eigenvalues of the Schr\"odinger type equations, within the context of Taylor expansion of a function. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical result for eigenvalues.