Accuracy of transfer matrix approaches for solving the effective mass Schr\"{o}dinger equation
Mesoscale and Nanoscale Physics
2011-06-17 v1 Computational Physics
Quantum Physics
Abstract
The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schr\"{o}dinger equation for arbitrary one-dimensional potentials, is investigated analytically and numerically. Both the case of a constant and a position dependent effective mass are considered. Comparisons with a finite difference method are also performed. Based on analytical model potentials as well as self-consistent Schr\"{o}dinger-Poisson simulations of a heterostructure device, it is shown that a symmetrized transfer matrix approach yields a similar accuracy as the Airy function method at a significantly reduced numerical cost, moreover avoiding the numerical problems associated with Airy functions.
Keywords
Cite
@article{arxiv.1106.3201,
title = {Accuracy of transfer matrix approaches for solving the effective mass Schr\"{o}dinger equation},
author = {Christian Jirauschek},
journal= {arXiv preprint arXiv:1106.3201},
year = {2011}
}