Exponentially confining potential well

TL;DR

This paper introduces an exponentially confining potential well as a model for strongly localized systems, providing approximate solutions for the Schrödinger equation using the Tridiagonal Representation Approach with Bessel polynomial basis.

Contribution

It presents a novel exponentially confining potential well and applies the TRA method to derive approximate energy spectra and wavefunctions for the system.

Findings

Lowest energy spectrum obtained

Wavefunctions expressed in Bessel polynomial basis

Method demonstrates effective approximation

Abstract

We introduce an exponentially confining potential well that could be used as a model to describe the structure of a strongly localized system. We obtain an approximate partial solution of the Schr\"odinger equation with this potential well where we find the lowest energy spectrum and corresponding wavefunctions. The Tridiagonal Representation Approach (TRA) is used as the method of solution, which is obtained as a finite series of square integrable functions written in terms of the Bessel polynomial.