Closed form solution for a double quantum well using Gröbner basis

Details Closed form solution for a double quantum well using Gröbner basis Closed form solution for a double quantum well using Gröbner basis

2011-06-28

arxiv.org/abs/1106.5987v1

Physics

Mathematical Physics

4 figures, Mathematica full calculation notebook

Scientific paper

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.

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