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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/2738

Title: Path integral quantization of the symmetric poschl-teller potential
Authors: Inomata, A.
Kayed, M.A.
Keywords: Path Integral quantization
Symmetric poschl-teller potential
Lie algebraic method
Issue Date: 11-Mar-1985
Publisher: Elsevier Science
Citation: Physics Letters: 108A (1); 9-12
Abstract: Feynman's path integral approach to quantum mechanics [I] is expected to be an alternative to Schrodinger's. Nevertheless, a limited number of problems have been solved exactly by path integration. It is a surprizing fact that such a typical example as the hydrogen atom has been left unsolved until very recently [2-41. Because of its gaussian (fresnellian) nature, the functional integral if represented in cartesian variables can be evaluated only for quadratic potentials [5]. Use of polar coordinates has helped to relax this limitation [6], placing the Infeld-Hull potential V= ar2 + br-* in the list of path-integable examples. However, the change of variables in path integrals is not trikial and the result is seldom beneficial to calculations. In recent years, some useful techniques have been devised, so that coordinate transformations are more effectively utilized to carry out path integration for the Aharonov-Bohm effect [7], the hydrogen atom [2,3], the Morse oscillator [8], the Dirac-Coulomb problem [4] and the charge-monopole system [9]. Now we are generally able to evaluate a path integral if it is intrinsically reducible in the local limit to a confluent hypergeometric equation of the Infeld-Hull type. It is interesting that this situation is parallel to that of the Sq2.1) dynarnical group approach [lo,) 11.
URI: http://hdl.handle.net/123456789/2738
ISSN: 0375-960
Appears in Collections:College of Science in Al-Kharj

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