Bound state energies of a particle in a finite square well: A simple approximation

James J. Murphy

Cyrus D. Cantrell

The energy eigenvalues for a particle bound in a finite or semi-infinite square-well potential are shown to be determined by the points of intersection of two straight lines with sine or cosine curves. This construction, which is simple enough for students to remember, can also be used to determine the number of bound states for a given potential strength, and to obtain approximate values for the energies of low-lying states in a deep square well.

Victor Bârsan

An approximate formula for the energy levels of the bound states of a particle in a finite square well are obtained, without using the Schrodinger equation. The physics and mathematics involved in this approach are accessible to a gifted high school student.

Forrest I. Glick

洋一 柴田

Orion Ciftja, Brett Johnston

Abstract We present details of a new solution method for the bound energy states of a quantum particle in a one-dimensional symmetric finite square well potential. The solution is obtained in a clear way by introducing a simple method that relies on the use of two auxiliary functions. The approach is straightforward and leads to the well-known even and odd parity wave function solutions of the problem without having to do any a priori assumptions about the nature or symmetry of the quantum states.