American Journal of Physics
We investigate the problem of a quantum particle in a one-dimensional finite square well. In the standard approach the allowed energies are determined implicitly as the solutions to a transcendental equation. We obtain the spectrum analytically as the solution to a pair of parametric equations and algebraically using a remarkably accurate approximation to the cosine function. The approach is also applied to a variety of other quantum wells.
Energy levels (Quantum mechanics); Quantum theory
Citation: Pilot Scholars Version (Modified MLA Style)
Bonfim, O. F. de Alcantara and Griffiths, David J., "Exact and approximate energy spectrum for the finite square well and related potentials" (2006). Physics Faculty Publications and Presentations. Paper 8.