Energy spectrum for trigonometric Pöschl–Teller potential

We present analytical solutions of the Schrödinger equation for the trigonometric Pöschl–Teller molecular potential by using a proper approximation to the centrifugal term within the framework of the asymptotic iteration method. We obtain analytic forms for the energy eigenvalues and the bound state...

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Bibliographic Details
Published inCanadian journal of physics Vol. 90; no. 12; pp. 1259 - 1265
Main Author Falaye, Babatunde James
Format Journal Article
LanguageEnglish
Published Ottawa NRC Research Press 01.12.2012
Canadian Science Publishing NRC Research Press
Subjects
03.65.Ge
03.65.–w
34.20.Cf
Approximation
Asymptotic methods
Asymptotic properties
Diatomic molecules
Eigenfunctions
Eigenvalues
Eigenvectors
Energy of formation
Energy spectra
Exact solutions
Hypergeometric functions
Iterative methods
Mathematical analysis
Mathematical functions
Mathematical physics
Molecules
Quantum numbers
Schrodinger equation
Schroedinger equation
Spectra (Spectroscopy)
Trigonometrical functions
Trigonometry
Nigeria
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Summary:We present analytical solutions of the Schrödinger equation for the trigonometric Pöschl–Teller molecular potential by using a proper approximation to the centrifugal term within the framework of the asymptotic iteration method. We obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the generalized hypergeometric functions. Energy eigenvalues for a few diatomic molecules are calculated for arbitrary quantum numbers n and ℓ with various values of parameter α. We also studied special case ℓ = 0 and found that the results are in good agreement with findings of other methods for short-range potential.
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ISSN:0008-4204
1208-6045
DOI:10.1139/p2012-103