Classical motion and coherent states for Pöschl–Teller potentials

The trigonometric and hyperbolic Pöschl–Teller potentials are dealt with from the point of view of classical and quantum mechanics. We show that there is a natural correspondence between the algebraic structure of these two approaches for both kind of potentials. Then, the coherent states are constructed and the appropriate classical variables are compared with the expected values of their corresponding quantum operators.