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Coherent states for nonlinear harmonic oscillator and some of its properties. (English) Zbl 1317.81153

Summary: 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.{
©American Institute of Physics}

MSC:

81R30 Coherent states
35Q55 NLS equations (nonlinear Schrödinger equations)
81Q15 Perturbation theories for operators and differential equations in quantum theory
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