Closed form solution for a double quantum well using Gröbner basis

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 Gröbner basis algorithm which allows to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.

4 figures, Mathematica full calculation notebook

Cited by in corpus (1)

• Bound states of the one-dimensional Dirac equation for scalar and vector double square-well potentials