×

The normalized wavefunctions of the Hartmann potential and explicit expressions for their radial average values. (English) Zbl 1005.81023

Summary: In this letter, we obtain the normalized polar angle wavefunctions and the normalized radial wavefunctions for the Hartmann potential in the spherical coordinate system. Two recurrence formulas for their radial average values are derived. The explicit functions \(\langle n^\prime l^\prime|r^s|n^\prime l^\prime\rangle\) are then listed for \(6\leqslant s\leqslant-3\).

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Hartmann, H., Theor. chim. acta, 24, 201, (1972)
[2] Hartmann, H.; Schuck, R.; Radtke, J., Theor. chim. acta, 46, 1, (1976)
[3] Hartmann, H.; Schuck, D., Int. J. quantum chem., 18, 125, (1980)
[4] Gerry, C.C., Phys. lett. A, 118, 445, (1986)
[5] Kibler, M.; Negadi, T., Int. J. quantum chem., 26, 405, (1984)
[6] Sökmen, I., Phys. lett. A, 115, 249, (1986)
[7] Kibler, M.; Negadi, T., Theor. chim. acta, 66, 31, (1984)
[8] Kibler, M.; Winternitz, P., J. phys. A, 20, 4097, (1987)
[9] Chen, C.-Y.; Sun, D.-S., Acta photonica sinica, 30, 104, (2001), (in Chinese)
[10] Chen, C.-Y.; Hu, S.Z., Acta physica sinica, 44, 9, (1995), (in Chinese)
[11] Wang, Z.X.; Guo, D.R., An introduction to special function, (1979), Science Press Beijing, Section 6.14 (in Chinese)
[12] Landau, L.D.; Lifshitz, E.M., Quantum mechanics (non-relativistic theory), (1979), Pregamon Press New York, Section 36 and following sections · Zbl 0178.57901
[13] Qian, B.C.; Zeng, J.Y., The problems choice and dissection in quantum mechanics, (1988), Science Press Beijing, p. 202 (in Chinese)
[14] Bockasten, K., Phys. rev. A, 9, 1087, (1974)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.