Symbolic-Numerical Algorithms for Solving Parabolic Quantum Well Problem with Hydrogen-Like Impurity

Authors:
S. I. Vinitsky;O. Chuluunbaatar;V. P. Gerdt;A. A. Gusev;V. A. Rostovtsev
Affiliations:
Joint Institute for Nuclear Research, Dubna, Russia;Joint Institute for Nuclear Research, Dubna, Russia;Joint Institute for Nuclear Research, Dubna, Russia;Joint Institute for Nuclear Research, Dubna, Russia;Joint Institute for Nuclear Research, Dubna, Russia
Venue:
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Year:
2009

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Abstract

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. 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.