Solution of Schrodinger equation using Tridiagonal representation approach in nonrelativistic quantum mechanics: a pedagogical approach

TL;DR

This paper introduces a pedagogical algebraic method called the Tridiagonal Representation Approach for solving the Schrödinger equation with various potentials, including a newly encountered three-parameter potential, enhancing understanding of quantum mechanics solutions.

Contribution

The paper presents a new pedagogical approach using the Tridiagonal Representation Method to solve Schrödinger equations, including a novel three-parameter potential example.

Findings

Successfully applied the method to a new three-parameter potential

Demonstrated the effectiveness of the approach for educational purposes

Provided explicit solutions for the Schrödinger equation with complex potentials

Abstract

We present the pedagogical method of Tridiagonal representation approach,an algebraic method for the solution of Schrodinger equation in nonrelativistic quantum mechanics for conventional potential functions. However, we solved a new three parameters potential function recently encountered using it as an example