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Exact solutions of the Schrödinger equation for the deformed hyperbolic potential well and the deformed four-parameter exponential type potential. (English) Zbl 1115.81332
Summary: Exact solutions of the Schrödinger equation for two ‘deformed hyperbolic potentials’ that were introduced by H. Arai [J. Math. Anal. Appl. 158, No. 1, 63–79 (1991; Zbl 0731.47055)] have been obtained by using an analytical solution method which has been developed by A. F. Nikiforov and V. B. Uvarov [Special Functions of Mathematical Physics. Basel: Birkhäuser (1988; Zbl 0624.33001)] for the solutions of the differential equations of hypergeometric type in which the solutions are special functions.
MSC:
81Q05Closed and approximate solutions to quantum-mechanical equations
33D90Applications of basic hypergeometric functions
34L40Particular ordinary differential operators