P\"oschl-Teller Hamiltonian: Gazeau-Klauder type coherent states, related statistics and geometry

This work mainly addresses a construction of Gazeau-Klauder type coherent states for a P"oschl-Teller model. Relevant characteristics are investigated. Induced geometry and statistics are studied. Then the Berezin - Klauder - Toeplitz quantization of the classical phase space observables is presented.