Wronskian method for bound states

TL;DR

This paper introduces a Wronskian-based method for calculating bound-state energies and wavefunctions in one-dimensional quantum mechanics, demonstrating its effectiveness with exactly solvable and Gaussian potential well examples.

Contribution

The paper presents a new, simple Wronskian approach for bound-state calculations, offering a straightforward alternative to existing methods.

Findings

Method accurately computes bound states in example models

Asymptotic analysis ensures correct energy determination

Applicable to various potential shapes

Abstract

We propose a simple and straightforward method based on Wronskians for the calculation of bound--state energies and wavefunctions of one--dimensional quantum--mechanical problems. We explicitly discuss the asymptotic behavior of the wavefunction and show that the allowed energies make the divergent part vanish. As illustrative examples we consider an exactly solvable model and the Gaussian potential well.