Five-parameter potential box with inverse square singular boundaries

TL;DR

This paper introduces a new five-parameter potential box with inverse square singularities at the boundaries and derives its energy spectrum and wavefunctions using the Tridiagonal Representation Approach.

Contribution

It presents a novel five-parameter potential model with inverse square singularities and provides analytical solutions using the Tridiagonal Representation Approach.

Findings

Analytical energy spectrum derived

Wavefunctions explicitly obtained

Potential model with inverse square singularities

Abstract

Using the Tridiagonal Representation Approach, we obtain solutions (energy spectrum and corresponding wavefunctions) for a new five-parameter potential box with inverse square singularity at the boundaries.