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arXiv:quant-ph/0312122 · International Journal of Modern Physics B

COHERENT AND GENERALIZED INTELLIGENT STATES FOR INFINITE SQUARE WELL POTENTIAL AND NONLINEAR OSCILLATORS

A. H. EL KINANI, Mohammed Daoud A

Published Oct 20, 2002• 9 citations
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Abstract

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system.1 We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau–Klauder and those à la Klauder–Perelomov, we derive the generalized intelligent states in analytical ways.

DOI
10.1142/s0217979202014656

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This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system.1 We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau–Klauder and those à la Klauder–Perelomov, we derive the generalized intelligent states in analytical ways.
The so-called Gazeau–Klauder and Perelomov coherent states are introduced for an arbitrary quantum system. We give also the general framework to construct the generalized intelligent states which minimize the Robertson–Schrödinger uncertainty relation. As illustration, the Pöschl–Teller potentials of trigonometric type will be chosen. We show the advantage of the analytical representations of Gazeau–Klauder and Perelomov coherent states in obtaining the generalized intelligent states in analytical way.
The construction of Generalized Intelligent States (GIS) for the x4x^4x4% -anharmonic oscillator is presented. These GIS families are required to minimize the Robertson-Schr\\"odinger 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.
We construct nonlinear coherent states or f -deformed coherent states for a nonpolynomial nonlinear oscillator which can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (Cariñena et al 2008 J. Phys. A: Math. Theor. 41 085301 ). The deformed annihilation and creation operators which are required to construct the nonlinear coherent states in the number basis are obtained from the solution of the Schrödinger equation. Using these operators, we construct generalized intelligent states, nonlinear coherent states, Gazeau–Klauder coherent states and the even and odd nonlinear coherent states for this newly solvable system. We also report certain nonclassical properties exhibited by these nonlinear coherent states. In addition to the above, we consider the position-dependent mass Schrödinger equation associated with this solvable nonlinear oscillator and construct nonlinear coherent states, Gazeau–Klauder coherent states and the even and odd nonlinear coherent states for it. We also give explicit expressions of all these nonlinear coherent states by considering a mass profile which is often used for studying transport properties in semiconductors.