Poeschl-Teller quantum oscillator and its limiting cases

TL;DR

This paper explores the Poeschl-Teller quantum oscillator model, demonstrating that its limiting cases include the quantum particle in a box and the harmonic oscillator, thus unifying these fundamental quantum models.

Contribution

It reveals that the Poeschl-Teller model encompasses two major quantum systems as limiting cases, providing a unified framework for understanding these models.

Findings

Poeschl-Teller model limits to quantum particle in a box

Poeschl-Teller model limits to quantum harmonic oscillator

Unification of key quantum models through limiting cases

Abstract

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.