Exact wave-function normalization constants for theB0tanhz−U0cosh−2zand Pöschl-Teller potentials

Abstract

We obtain, in exact closed form, the wave-function normalization constants for the Schr\odinger equation with potential $V={B}_{0}tanhz\ensuremath{-}{U}_{0}{cosh}^{\ensuremath{-}2}z$. These constants are derived in terms of a variety of formulations and solutions of the equation. We give discussions of both mathematical aspects and physical motivations of the problem. The main results are gathered in two appendixes. Wave-function normalization constants for the related P\oschl-Teller potential are given in a third appendix.