Acta Physica Sinica

Symmetry in spectrum space of isotonic oscillator and two-photon parametric model

Wenbo Li, Kexuan Li, Ye Li, Li Mi-Shan, Yaling Li, Wen Xiao-Yang, Yuan Guang-Jun, 北京交通大学物理系,北京　100044

Published Jan 1, 2004• 1 citation

Abstract

Symmetry in spectrum space of isotonic oscillators is studied, and a distinct fi gure is given by appropriate parametric substitution. An analytic expression of normalized eigenfunction is obtained. It is proven that linear oscillator is a degeneration of isotonic oscillator. It is revealed that an isotonic oscillator is a two_photon parametric model. Coherent state of that model is given, and that coherent state includes odd_coherent state and even_coherent state constru cted by Glauber coherent states in a natural way.

DOI: 10.7498/aps.53.4202

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Acta Physica Sinica

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Published Jan 1, 2004• 1 citation

Publisher

Abstract

DOI: 10.7498/aps.53.4202

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Abstract We construct a new class of nonlinear coherent states for the isotonic oscillator by replacing the factorial of the coefficients z n / n !

{z}^{n}/\sqrt{n!}

of the canonical coherent states by the factorial x n γ ! = x 1 γ . x 2 γ … x n γ

{x}_{n}^{\gamma }!={x}_{1}^{\gamma }.{x}_{2}^{\gamma }\dots {x}_{n}^{\gamma }

with x 0 γ = 0

{x}_{0}^{\gamma }=0

, where x n γ

{x}_{n}^{\gamma }

is a sequence of positive numbers and γ is a positive real parameter. This also leads to the construction of a Bargmann-type integral transform which will allow us to find some integral transforms for orthogonal polynomials. The statistics of our coherent states will also be considered by the calculus of one called Mandel parameter. The squeezing phenomenon was also discussed.