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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kazaryan, E.M., Kostanyan, A.A., Sarkisyan, H.: Impurity optical absorption in parabolic quantim well. Physica E 28, 423–430 (2005)
Voss, H.: Numerical calculation of the electronic structure for three-dimensional quantum dots. Comput. Phys. Commun. 174, 441–446 (2006)
Wang, W., Hwang, T.-M., Jang, J.-C.: A second-order finite volume scheme for three dimensional truncated pyramidal quantum dot. Comput. Phys. Commun. 174, 371–385 (2006)
Gusev, A.A., Chuluunbaatar, O., Vinitsky, S.I., Derbov, V.L., Kazaryan, E.M., Kostanyan, A.A., Sarkisyan, H.A.: Adiabatic approach to the problem of a quantum well with a hydrogen – like impurity. Phys. Atomic Nuclei 72, 1600–1608 (2010)
Chuluunbaatar, O., Gusev, A.A., Abrashkevich, A.G., Amaya-Tapia, A., Kaschiev, M.S., Larsen, S.Y., Vinitsky, S.I.: KANTBP: A program for computing energy levels, reac-tion matrix and radial wave functions in the coupled-channel hyperspherical adia-batic approach. Comput. Phys. Commun. 177, 649–675 (2007)
Chuluunbaatar, O., Gusev, A.A., Gerdt, V.P., Rostovtsev, V.A., Vinitsky, S.I., Abrashkevich, A.G., Kaschiev, M.S., Serov, V.V.: POTHMF: A program for computing potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field. Comput. Phys. Commun. 178, 301–330 (2008)
Chuluunbaatar, O., Gusev, A.A., Vinitsky, S.I., Abrashkevich, A.G.: KANTBP 2.0: New version of a program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach. Comput. Phys. Commun. 179, 685–693 (2008)
Gusev, A.I., Rempel, A.A.: Nanocrystalline materials. Cambridge Int. Sci, Cambridge (2004)
Chuluunbaatar, O., Gusev, A.A., Vinitsky, S.I., Abrashkevich, A.G.: ODPEVP: A program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem. Accepted in Comput. Phys. Commun. (2009), 10.1016/j.cpc.2009.04.017
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1972)
Barnett, A.R.: KLEIN: Coulomb functions for real λ and positive energy of high accuracy. Comput. Phys. Commun. 24, 141–159 (1981)
Barnett, A.R., Feng, D.H., Steed, J.W., Goldfarb, L.J.B.: Coulomb wave functions for all real η and ρ. Comput. Phys. Comm. 8, 377–395 (1974)
Epstein, S.T.: Ground state energy of a molecule in adiabatic approximation. J. Chem. Phys. 144, 836–837 (1965)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vinitsky, S.I., Chuluunbaatar, O., Gerdt, V.P., Gusev, A.A., Rostovtsev, V.A. (2009). Symbolic-Numerical Algorithms for Solving Parabolic Quantum Well Problem with Hydrogen-Like Impurity. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-04103-7_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04102-0
Online ISBN: 978-3-642-04103-7
eBook Packages: Computer ScienceComputer Science (R0)