Infinite potential well with a sinusoidal bottom
Quantum Physics
2022-06-20 v1
Abstract
We construct a tridiagonal matrix representation of the wave operator that maps the wave equation into a three-term recursion relation for the expansion coefficients of the wavefunction. Finding a solution of the recursion relation is equivalent to solving the original problem. Consequently, a larger class of solvable potentials is obtained. The usual diagonal representation constraint results in a reduction to the conventional class of solvable potentials. To exhibit the power of this approach, we give an exact solution for the infinite potential well with sinusoidal bottom.
Keywords
Cite
@article{arxiv.0808.1006,
title = {Infinite potential well with a sinusoidal bottom},
author = {A. D. Alhaidari and H. Bahlouli},
journal= {arXiv preprint arXiv:0808.1006},
year = {2022}
}
Comments
8 pages, 2 figures, 1 table Details will be published in Journal of Mathematical Physics, Vol. 49, Issue 8 (August 2008)