Complexifier Versus Factorization and Deformation Methods For Generation of Coherent States of a 1D NLHO: I. Mathematical Construction

Three methods: complexifier, factorization and deformation, for construction of coherent states are presented for one dimensional nonlinear harmonic oscillator (1D NLHO). Since by exploring the Jacobi polynomials $P_n^{a,b}$'s, bridging the difference between them is possible, we give here also the exact solution of Schr\"odinger equation of 1D NLHO in terms of Jacobi polynomials.Comment: To be Published in: Int. J. Geom. Meth. Mod. Physic

Analogue Special and General Relativity by Optical Multilayer Thin Films: The Rindler Space Case

In this paper, to obtain an analogy between the curved spaces and the linear optics, we expand the idea of Ref.[1, 2] to the multilayer films. We investigate efects of thickness and index of refraction of the films on the Lorentzian transformations. In addition, by using the multilayer films, we suggest very simple experimental set-up which can serve as an analogue computer for testing special relativity. Finally, we draw an analogy between the Rindler space, as an example of the curved spaces, and a suitable multilayer film.Comment: 5 Figure

Gazeau−-Klauder squeezed states associated with solvable quantum systems

A formalism for the construction of some classes of Gazeau$-$Klauder squeezed states, corresponding to arbitrary solvable quantum systems with a known discrete spectrum, are introduced. As some physical applications, the proposed structure is applied to a few known quantum systems and then statistical properties as well as squeezing of the obtained squeezed states are studied. Finally, numerical results are presented.Comment: 18 pages, 12 figure