Abstract
An algorithm for symbolic calculation of eigenvalues and eigenfunctions of a hydrogen atom in weak electric fields is suggested. A perturbation theory scheme is constructed that is based on an irreducible infinite-dimensional representation of algebra so(4, 2) of the group of dynamical symmetry for the hydrogen atom [1]. The scheme implementation does not rely on the assumption that the independent variables of the perturbation operator can be separated, and fractional powers of parabolic quantum numbers are not used in the recurrent relations determining the operation of algebra generators on the corresponding basis of the irreducible representation [2]. A seventh-order correction to the energy spectrum of the hydrogen atom in a uniform electric field is given. The algorithm suggested is implemented in REDUCE 3.6 [4].
Similar content being viewed by others
REFERENCES
Malkin, I.A. and Man'ko, V.I., Dinamicheskaya simmetriya i kogerentnye sostoyaniya kvantovykh sistem (Dynamical Symmetry and Coherent States of Quantum Systems), Moscow: Nauka, 1979.
Kadomtsev, M.B. and Vinitsky, S.I., Perturbation Theory within the O(4, 2) Group for a Hydrogen-like Atom, J. Phys. A, 1985, vol. 18, pp. L689-L695.
Adams, B.G., Unified Treatment of High-Order Perturbation Theory for the Stark Effect in a Two-and Three-Dimensional Hydrogen Atom, Phys. Rev. A, 1992, vol. 46, no. 7, pp. 4060-4064.
Hearn, A.C., Reduce: User's Manual, version 3.6, Santa Monica, CA, 1995.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gusev, A.A., Samoilov, V.N., Rostovtsev, V.A. et al. Algebraic Perturbation Theory for Hydrogen Atom in Weak Electric Fields. Programming and Computer Software 27, 18–21 (2001). https://doi.org/10.1023/A:1007178501538
Issue Date:
DOI: https://doi.org/10.1023/A:1007178501538