Square wells, quantum wells and ultra-thin metallic films

TL;DR

This paper derives exact and approximate solutions for bound state energies in square wells, with applications to quantum wells, ultra-thin metallic films, and related resonant systems.

Contribution

It provides exact power series solutions and accurate approximations for eigenvalues in square wells, enhancing understanding of quantum well physics and applications.

Findings

Exact eigenvalue solutions for square wells

Analytical approximations for bound state energies

Applications to ultra-thin metallic films and resonant systems

Abstract

The eigenvalue equations for the energy of bound states of a particle in a square well are solved, and the exact solutions are obtained, as power series. Accurate analytical approximate solutions are also given. The application of these results in the physics of quantum wells are discussed,especially for ultra-thin metallic films, but also in the case of resonant cavities, heterojunction lasers, revivals and super-revivals.