Generalized Intelligent States for Nonlinear Oscillators

Abstract

The construction of Generalized Intelligent States (GIS) for the $x^4$% -anharmonic oscillator is presented. These GIS families are required to minimize the Robertson-Schrödinger uncertainty relation. As a particular case, we will get the so-called Gazeau-Klauder coherent states. The properties of the latters are discussed in detail. Analytical representation is also considered and its advantage is shown in obtaining the GIS in an analytical way. Further extensions are finally proposed.

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Cited by in corpus (16)

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• Photon-added coherent states for exactly solvable Hamiltonians
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• Coherent and squeezed states: introductory review of basic notions, properties and generalizations
• Nonlinear Quantum Optical Springs and Their Nonclassical Properties
• A Generalized Jaynes-Cummings Model: Nonlinear dynamical superalgebra $u(1/1)$ and Supercoherent states
• The Moyal Bracket in the Coherent States framework
• Superpositions of the dual family of nonlinear coherent states and their non-classical properties
• Coherent and generalized intelligent states for infinite square well potential and nonlinear oscillators
• Quantum statistical properties of some new classes of intelligent states associated with special quantum systems
• Generalized intelligent states of the su(N) algebra
• Robertson-Schrödinger intelligent states for two-body Calogero model
• Analytic representations based on su(3) coherent states and Robertson intelligent states
• Generalized Grassmann variables for quantum kit (k-level) systems and Barut-Girardello coherent states for su(r+1) algebras