Unified path integral treatment for generalized Hulthén and Woods–Saxon potentials

• Published in: Annals of physics Vol. 322; no. 9; pp. 2179 - 2194
• Main Authors: Benamira, F., Guechi, L., Mameri, S., Sadoun, M.A.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.09.2007; Elsevier BV
• Subjects: BOUND STATE; Bound states; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENERGY SPECTRA; EQUATIONS; Generalized Hulthén potential; Generalized Woods–Saxon potential; GREEN FUNCTION; HULTHEN POTENTIAL; Mathematics; Molecules; MORSE POTENTIAL; NUMERICAL SOLUTION; Path integral; PATH INTEGRALS; Physics; QUANTIZATION; S STATES; WAVE FUNCTIONS; WOODS-SAXON POTENTIAL; Generalized Woods–Saxon potential; 03.65.Db-Functional analytical methods; Generalized Hulthén potential; 03.65.Ca-Formalism; Path integral; Morse potential; Bound states
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2007.01.011

A rigorous path integral discussion of the s states for a diatomic molecule potential with varying shape, which generalizes the Hulthén and the Woods–Saxon potentials, is presented. A closed form of the Green’s function is obtained for different shapes of this potential. For λ ⩾ 1 and ( 1 / η ) ln λ < r < ∞ , the energy spectrum and the normalized wave functions of the bound states are derived. When the deformation parameter λ is 0 < λ < 1 or λ < 0, it is found that the quantization conditions are transcendental equations that require numerical solutions. The special cases corresponding to a screened potential ( λ = 1), the deformed Woods–Saxon potential ( λ = q e ηR ), and the Morse potential ( λ = 0) are likewise treated.