Unified path integral treatment for generalized Hulthen and Woods-Saxon potentials

Journal Article · Sat Sep 15 00:00:00 EDT 2007 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2007.01.011· OSTI ID:20976797

Benamira, F ^[1]; Guechi, L ^[1]; Mameri, S ^[1]; Sadoun, M A ^[1]

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1. Laboratoire de Physique Theorique, Departement de Physique, Faculte des Sciences Exactes, Universite Mentouri, Route d'Ain El Bey, Constantine (Algeria)

A rigorous path integral discussion of the s states for a diatomic molecule potential with varying shape, which generalizes the Hulthen and the Woods-Saxon potentials, is presented. A closed form of the Green's function is obtained for different shapes of this potential. For {lambda}>=1 and (1/{eta})ln{lambda}<r<{approx}, the energy spectrum and the normalized wave functions of the bound states are derived. When the deformation parameter {lambda} is 0<{lambda}<1 or {lambda}<0, it is found that the quantization conditions are transcendental equations that require numerical solutions. The special cases corresponding to a screened potential ({lambda}=1), the deformed Woods-Saxon potential ({lambda}=qe{sup {eta}}{sup R}), and the Morse potential ({lambda}=0) are likewise treated.

• OSTI ID: 20976797
• Journal Information: Annals of Physics (New York), Vol. 322, Issue 9; Other Information: DOI: 10.1016/j.aop.2007.01.011; PII: S0003-4916(07)00019-X; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUND STATE
ENERGY SPECTRA
EQUATIONS
GREEN FUNCTION
HULTHEN POTENTIAL
MORSE POTENTIAL
NUMERICAL SOLUTION
PATH INTEGRALS
QUANTIZATION
S STATES
WAVE FUNCTIONS
WOODS-SAXON POTENTIAL