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arXiv:0902.4574 · Modern Physics Letters A

COHERENT STATE OF THE EFFECTIVE MASS HARMONIC OSCILLATOR

Atreyee Biswas, Barnana Roy

Published Jun 7, 2009• 9 citations
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Abstract

We construct coherent state of the effective mass harmonic oscillator and examine some of its properties. In particular closed form expressions of coherent states for different choices of the mass function are obtained and it is shown that such states are not in general x - p uncertainty states. We also compute the associated Wigner functions.

DOI
10.1142/s0217732309028977

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We construct coherent state of the effective mass harmonic oscillator and examine some of its properties. In particular closed form expressions of coherent states for different choices of the mass function are obtained and it is shown that such states are not in general x - p uncertainty states. We also compute the associated Wigner functions.
Abstract We present details of the method for constructing the coherent states of the quantum harmonic oscillator model that exhibits the semiconfinement effect due to a specific change of its mass by position. Its energy spectrum completely overlaps with the Hermite oscillator energy spectrum, whereas the wavefunctions of the stationary states are expressed via the generalized Laguerre polynomials. Two different methods have been applied to compute the coherent states. They are generalized and Barut-Girardello coherent states methods. In both cases, the exact expressions have been obtained. We also analyzed some limit cases, under which the constructed coherent states completely recover the coherent states of the Hermite oscillator.
We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties for the system with PDM are also discussed. We give the corresponding effective potentials for several mass functions, the systems with such potentials are isospectral to the usual harmonic oscillator.
In this paper, dynamics and quantum mechanical coherent states of a simple harmonic oscillator are considered in the framework of the Generalized Uncertainty Principle (GUP). Equations of motion for the simple harmonic oscillator are derived and some of their new implications are discussed. Then, coherent states of the harmonic oscillator in the case of the GUP are compared with the relative situation in ordinary quantum mechanics. It is shown that in the framework of GUP there is no considerable difference in definition of coherent states relative to ordinary quantum mechanics. But, considering expectation values and variances of some operators, based on quantum gravitational arguments, one concludes that although it is possible to have complete coherency and vanishing broadening in usual quantum mechanics, gravitational induced uncertainty destroys complete coherency in quantum gravity and it is not possible to have a monochromatic ray in principle.
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.