A New Methodology for the Development of Numerical Methods for the Numerical Solution of the Schr\"odinger Equation

TL;DR

This paper introduces a novel methodology for developing numerical methods to solve the one-dimensional Schrödinger equation, focusing on minimizing phase-lag and its derivatives to improve accuracy, validated through error analysis and numerical tests.

Contribution

The paper presents a new approach based on phase-lag elimination for constructing more accurate numerical methods for the Schrödinger equation.

Findings

Enhanced accuracy demonstrated through error analysis.

Numerical applications confirm the effectiveness of the new methods.

Method reduces phase-lag effects compared to traditional approaches.

Abstract

In the present paper we introduce a new methodology for the construction of numerical methods for the approximate solution of the one-dimensional Schr\"odinger equation. The new methodology is based on the requirement of vanishing the phase-lag and its derivatives. The efficiency of the new methodology is proved via error analysis and numerical applications.