Modified Hamiltonian for a particle in an infinite box that includes wall effects

TL;DR

This paper introduces a modified Hamiltonian for a particle in an infinite potential box that incorporates wall effects, providing a new formulation in both position and momentum representations.

Contribution

It presents a novel Hamiltonian that accounts for wall effects in an infinite potential well, with formulations in position and momentum space.

Findings

Eigenvalue problem becomes an integral equation in momentum space

Modified Hamiltonian explicitly includes wall effects

Provides new insights into particle behavior in confined systems

Abstract

We give a modified Hamiltonian for a particle in a box with infinite potential walls that takes into account wall effects. The Hamiltonian is expressed in both the position and momentum representation. In the momentum representation the eigenvalue problem for energy is an integral equation.