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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].

81-08 Computational methods for problems pertaining to quantum theory
68W30 Symbolic computation and algebraic computation
Full Text: DOI
[1] Kazaryan, E.M., Kostanyan, A.A., Sarkisyan, H.: Impurity optical absorption in parabolic quantim well. Physica E 28, 423–430 (2005) · doi:10.1016/j.physe.2005.05.047
[2] Voss, H.: Numerical calculation of the electronic structure for three-dimensional quantum dots. Comput. Phys. Commun. 174, 441–446 (2006) · Zbl 1196.65099 · doi:10.1016/j.cpc.2005.12.003
[3] 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) · Zbl 1196.81078 · doi:10.1016/j.cpc.2005.10.012
[4] 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)
[5] 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) · Zbl 1196.81283 · doi:10.1016/j.cpc.2007.05.016
[6] 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) · Zbl 1196.65175 · doi:10.1016/j.cpc.2007.09.005
[7] 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) · Zbl 1197.81008 · doi:10.1016/j.cpc.2008.06.005
[8] Gusev, A.I., Rempel, A.A.: Nanocrystalline materials. Cambridge Int. Sci, Cambridge (2004) · doi:10.1201/9781439834398.ch178
[9] 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 · Zbl 1198.15002 · doi:10.1016/j.cpc.2009.04.017
[10] Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1972) · Zbl 0543.33001
[11] Barnett, A.R.: KLEIN: Coulomb functions for real \(\lambda\) and positive energy of high accuracy. Comput. Phys. Commun. 24, 141–159 (1981) · doi:10.1016/0010-4655(81)90088-6
[12] Barnett, A.R., Feng, D.H., Steed, J.W., Goldfarb, L.J.B.: Coulomb wave functions for all real \(\eta\) and \(\rho\). Comput. Phys. Comm. 8, 377–395 (1974) · doi:10.1016/0010-4655(74)90013-7
[13] Epstein, S.T.: Ground state energy of a molecule in adiabatic approximation. J. Chem. Phys. 144, 836–837 (1965)
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