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

We obtain, in exact closed form, the wave-function normalization constants for the Schrödinger equation with potential $V=B_{0}tanhz-U_0{cosh}^{-2\mathrm{}}z$. 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 Pöschl-Teller potential are given in a third appendix.