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Scattering states of Schrödinger equation under the modified cusp potential. (English) Zbl 1284.81119

Summary: We solve the one-dimensional time-independent Schrödinger equation in the presence of the modified cusp potential and report the solutions in terms of the Whittaker functions. We obtain the reflection and transmission coefficients as well as the bound-state solutions in terms of the Whittaker functions. We comment on the solutions and discuss them in terms of the engaged parameters.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
81U99 Quantum scattering theory
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