Abstract
A simple and straightforward calculating scheme is suggested for finding wave functions of the hydrogen atom in prolate spheroidal coordinates. The wave functions are found in an explicit form by the direct solution of appropriate one-dimensional equations. The suggested calculating scheme allows us to carry out simple calculations and to obtain spheroidal wave functions in principle for arbitrary eigenstates of the hydrogen atom. Expansions are found for the obtained spheroidal wave functions over a spherical basis.
References
C.A. Coulson, P.D. Robinson, Proc. Phys. Soc. 71, 815 (1958)
J.D. Power, Phil. Trans. Roy. Soc. A 274, 663 (1973)
I.V. Komarov, L.I. Ponimarev, S.Yu. Slavyanov, Spheroidal and Coulomb Spheroidal Functions (Moscow, Nauka, 1976) (in Russian)
S.M. Sung, D.R. Herschbach, J. Chem. Phys. 95, 7437 (1991)
C.A. Coulson, A. Joseph, Proc. Phys. Soc. 90, 887 (1967)
B.E. Granger, E.L. Hamilton, C.H. Greene, Phys. Rev. A 64, 042508 (2001)
L.G. Mardoyan, G.S. Pogosyan, A.N. Sissakyan, V.M. Ter-Antonyan, J. Phys. A 16, 711 (1983)
L.G. Mardoyan, G.S. Pogosyan, A.N. Sissakyan, V.M. Ter-Antonyan, Teor. Mat. Fiz. 64, 171 (1985)
T.M. Kerezelidze, Bull. Acad. Sci. Georgian SSR 139, 481 (1990)
M.I. Chibisov, T.M. Kereselidze, Preprint IAE-5410/6 (I.V. Kurchatov Institute of Atomic Energy, Moscow, 1991), pp. 1 − 43
T.M. Kerezelidze, Z.S. Machavariani, I.L. Noselidze, J. Phys. B At. Mol. Opt. Phys. 29, 257 (1996)
T.M. Kerezelidze, Z.S. Machavariani, I.L. Noselidze, J. Phys. B At. Mol. Opt. Phys. 31, 15 (1998)
L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (New York, Pergamon, 1977)
D. Park, Z. Phys. 159, 155 (1960)
S.S. Gerstein, V.D. Krivchenkov, Sov. Phys. JETP 13, 1044 (1961)
A.Z. Devdariani, T.M. Kereselidze, I.L. Noselidze, E. Dalimier, P. Sauvan, P. Angelo, R. Schott, Phys. Rev. A 71, 022512 (2005)
P.D. Robinson, Proc. Phys. Soc. 71, 828 (1958)
T.P. Grozdanov , E.A. Solov’ev , Phys. Rev. A 51, 2630 (1995)
C.H. Greene, A.S. Dickinson, H.R. Sadeghpour, Phys. Rev. Lett. 85, 2458 (2000)
M.I. Chibisov, A.A. Khuskivadze, I.I. Fabrikant, J. Phys. B At. Mol. Opt. Phys. 35, L1 (2002)
M.I. Chibisov, Usp. Fiz. Nauk 172, 1 (2002)
M.I. Chibisov, Phys.-Usp. 45, 1 (2002)
T.M. Kereselidze, J. Phys. B 20, 1891 (1987)
G.A. Korn, T.M. Korn, Mathematical Handbook for Scientists and Engineers (Mgraw-Hill Book Company, Inc. New York Toronto London, 1961)
A.G. Kurosh, Course of Higher Algebra (Moscow, Gostekhizdat, 1952) (in Russian)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kereselidze, T., Machavariani, Z.S. & Chkadua, G. Explicit spheroidal wave functions of the hydrogen atom. Eur. Phys. J. D 63, 81–87 (2011). https://doi.org/10.1140/epjd/e2011-10690-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjd/e2011-10690-6