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Bound and scattering states for a hyperbolic‐type potential in view of a new developed approximation
Author(s) -
Aydoğdu Oktay,
Yanar Hilmi
Publication year - 2015
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.24886
Subject(s) - bound state , eigenvalues and eigenvectors , hypergeometric function , scattering , wave function , scattering amplitude , scattering theory , amplitude , mathematical analysis , jacobi polynomials , physics , function (biology) , energy (signal processing) , schrödinger equation , quantum mechanics , mathematics , orthogonal polynomials , evolutionary biology , biology
A new developed approximation is used to obtain the arbitrary l ‐wave bound and scattering state solutions of Schrödinger equation for a particle in a hyperbolic‐type potential. For bound state, the energy eigenvalue equation and unnormalized wave functions in terms of Jacobi polynomials are achieved using the Nikiforov–Uvarov (NU) method. Besides, energy eigenvalues are calculated numerically for some states and compared with those given in the literature to check accuracy of our results. For scattering state, the wave function is found in terms of hypergeometric functions. Furthermore, scattering amplitude and phase shifts are achieved using scattering solutions. Also it is shown that the energy eigenvalue equation obtained from analytic property of scattering amplitude is same with one obtained using NU method. © 2015 Wiley Periodicals, Inc.