Exact Polynomial Solutions of Schrödinger Equation with Various Hyperbolic Potentials

The Schrodinger equation with hyperbolic potential V(x) = - V sub(0)sinh super(2q)(x/d)/cos h super(6)(x/d) (q = 0,1, 2, 3) is studied by transforming it into the confluent Heun equation. We obtain general symmetric and antisymmetric polynomial solutions of the Schrodinger equation in a unified form...

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Bibliographic Details
Published in:Communications in theoretical physics 2014-02, Vol.61 (2), p.153-159
Main Authors: Wen, Fa-Kai, Yang, Zhan-Ying, Liu, Chong, Yang, Wen-Li, Zhang, Yao-Zhong
Format: Article
Language:English
Subjects:
Mathematical analysis
Polynomials
Schroedinger equation
Strength
Symmetry
Theoretical physics
Wavefunctions
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Summary:The Schrodinger equation with hyperbolic potential V(x) = - V sub(0)sinh super(2q)(x/d)/cos h super(6)(x/d) (q = 0,1, 2, 3) is studied by transforming it into the confluent Heun equation. We obtain general symmetric and antisymmetric polynomial solutions of the Schrodinger equation in a unified form via the Functional Bethe ansatz method. Furthermore, we discuss the characteristic of wavefunction of bound state with varying potential strengths. Particularly, the number of wavefunction's nodes decreases with the increase of potential strengths, and the particle tends to the bottom of the potential well correspondingly.
ISSN:0253-6102
1572-9494
DOI:10.1088/0253-6102/61/2/02