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Symbolic-numerical algorithms for solving parabolic quantum well problem with hydrogen-like impurity. (English) Zbl 1239.81008
Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 11th international workshop, CASC 2009, Kobe, Japan, September 13–17, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-04102-0/pbk). Lecture Notes in Computer Science 5743, 334-349 (2009).
Summary: For parabolic quantum well problem with hydrogen-like impurity a two-dimensional boundary-value problem is formulated in spherical coordinates at fixed magnetic quantum number. A calculational scheme using modified angular prolate spheroidal functions is presented. Symbolic-numerical algorithms for solving the problem are elaborated. The efficiency of the algorithms and their implementation is demonstrated by solving typical test examples and proving the compatibility conditions for asymptotic solutions of scattering problems in spherical and cylindrical coordinates.
For the entire collection see [Zbl 1175.68009].

MSC:
81-08 Computational methods for problems pertaining to quantum theory
68W30 Symbolic computation and algebraic computation
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