Eur. Phys. J. Plus (2016) 131: 43
https://doi.org/10.1140/epjp/i2016-16043-5

Regular Article

Gazeau-Klauder coherent states for the partner potentials of the trigonometric symmetric scarf type

Department of Theoretical Physics and Astrophysics, Faculty of Physics, University of Tabriz, P. O. Box 51666-16471, Tabriz, Iran

^* e-mail: hfakhri@tabrizu.ac.ir

Received: 18 December 2015
Accepted: 22 January 2016
Published online: 23 February 2016

Abstract

The supersymmetric partner Schrödinger equations for the superpotential with A as non-negative integers are solved by using the Darboux factorization method on the associated Romanovski differential equation. The bound states correspond to a particle which is trapped on the bounded interval and their number is infinite. Its partner Hamiltonians are iso-spectral except for the ground state which, in turn, leads us to associate different Gazeau-Klauder coherent states for each of the partner potentials with different positive definite measures to realize the resolution of identity condition. It is shown that the time evolution does not change the form of the Gazeau-Klauder coherent states. Furthermore, it is discussed that the weight distribution functions of each of the coherent states obey the sub-Poissonian statistics. Finally, Gazeau-Klauder cat states are introduced for one of the partner potentials.