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NONLINEAR COHERENT STATES FOR PSEUDOHARMONIC OSCILLATOR

Ioan Zaharie, Dušan Popov

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The aim of this work is to construct nonlinear coherent states of the pseudo-harmonic oscillator and to analyze some of its properties. The pseudo-harmonic potential can be viewed as an intermediate case between the harmonic and inharmonic potentials. The fact allows the implementation (with notable results), for inharmonic potentials, of some methods well known for harmonic potentials. An example is represented by the construction of nonlinear coherent states, which in the case of harmonic oscillator has found a lot of applications.

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A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.