Poeschl-Teller quantum oscillator and its limiting cases

One of the most interesting models of the nonrelativistic quantum mechanics (in one-dimensional case) introduced by G. Poeschl and E.Teller at 1933 is considered. It is shown that this model possesses as its limiting cases two most popular quantum models: the quasi-free quantum particle in the box as well as the quantum harmonic oscillator introduced by F. Bloch at 1932.