Semi-classical behavior of P\"oschl-Teller coherent states

TL;DR

This paper constructs semi-classical coherent states for P"oschl-Teller potentials using supersymmetric quantum mechanics, which bridge classical and quantum descriptions and exhibit localized time evolution.

Contribution

It introduces a novel method to build semi-classical states for P"oschl-Teller potentials that satisfy key properties like uncertainty minimization and phase space localization.

Findings

States minimize a special uncertainty relation

States resolve the identity with a uniform measure

Time evolution remains localized on classical trajectories

Abstract

We present a construction of semi-classical states for P\"oschl-Teller potentials based on a supersymmetric quantum mechanics approach. The parameters of these "coherent" states are points in the classical phase space of these systems. They minimize a special uncertainty relation. Like standard coherent states they resolve the identity with a uniform measure. They permit to establish the correspondence (quantization) between classical and quantum quantities. Finally, their time evolution is localized on the classical phase space trajectory.