Closed form solution for a double quantum well using Gr\"obner basis
Mathematical Physics
2015-05-28 v1 math.MP
Computational Physics
Abstract
Analytical expressions for spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and effective masses are different. This was achieved by Gr\"obner basis algorithm which allows to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.
Cite
@article{arxiv.1106.5987,
title = {Closed form solution for a double quantum well using Gr\"obner basis},
author = {A. Acus and A. Dargys},
journal= {arXiv preprint arXiv:1106.5987},
year = {2015}
}
Comments
4 figures, Mathematica full calculation notebook