Approach of the Generating Functions to the Coherent States for Some Quantum Solvable Models

We introduce to this paper new kinds of coherent states for some quantum solvable models: a free particle on a sphere, one-dimensional Calogero-Sutherland model, the motion of spinless electrons subjected to a perpendicular magnetic field B, respectively, in two dimensional flat surface and an infinite flat band. We explain how these states come directly from the generating functions of the certain families of classical orthogonal polynomials without the complexity of the algebraic approaches. We have shown that some examples become consistent with the Klauder- Perelomove and the Barut-Girardello coherent states. It can be extended to the non-classical, q-orthogonal and the exceptional orthogonal polynomials, too. Especially for physical systems that they don't have a specific algebraic structure or involved with the shape invariance symmetries, too.Comment: 16 page

Generalized su(2)su(2) coherent states for the Landau levels and their nonclassical properties

Following the lines of the recent papers [J. Phys. A: Math. Theor. 44, 495201 (2012); Eur. Phys. J. D 67, 179 (2013)], we construct here a new class of generalized coherent states related to the Landau levels, which can be used as the finite Fock subspaces for the representation of the $su(2)$ Lie algebra. We establish the relationship between them and the deformed truncated coherent states. We have, also, shown that they satisfy the resolution of the identity property through a positive definite measures on the complex plane. Their nonclassical and quantum statistical properties such as quadrature squeezing, higher order `$su(2)$' squeezing, anti-bunching and anti-correlation effects are studied in details. Particularly, the influence of the generalization on the nonclassical properties of two modes is clarified.Comment: arXiv admin note: text overlap with arXiv:1212.6888, arXiv:1404.327

Generalized su(1,1)su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties

In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is that, contrary to the Klauder-Perelomov and Barut-Girardello approaches, it does not require the existence of dynamical symmetries associated with the system under consideration. These states admit a resolution of the identity through positive definite measures on the complex plane. We have shown that the realization of these states for different values of the deformation parameters leads to the well-known Klauder-Perelomov and Barut-Girardello CSs associated with the $su(1,1)$ Lie algebra. This is why we call them the generalized $su(1,1)$ CSs for the PHO. Finally, study of some statistical characters such as squeezing, anti-bunching effect and sub-Poissonian statistics reveals that the constructed GCSs have indeed nonclassical features.Comment: arXiv admin note: substantial text overlap with arXiv:1212.688

Landau Levels as a Limiting Case of a Model with the Morse-Like Magnetic Field

We consider the quantum mechanics of an electron trapped on an infinite band along the $x$-axis in the presence of the Morse-like perpendicular magnetic field $\vec{B}=-B_{0}e^{-\frac{2\pi}{a_{0}}x}\hat{k}$ with $B_{0}>0$ as a constant strength and $a_{0}$ as the width of the band. It is shown that the square integrable pure states realize representations of $su(1,1)$ algebra via the quantum number corresponding to the linear momentum in the $y$-direction. The energy of the states increases by decreasing the width $a_{0}$ while it is not changed by $B_{0}$. It is quadratic in terms of two quantum numbers, and the linear spectrum of the Landau levels is obtained as a limiting case of $a_{0}\rightarrow\infty$. All of the lowest states of the $su(1,1)$ representations minimize uncertainty relation and the minimizing of their second and third states is transformed to that of the Landau levels in the limit $a_{0}\rightarrow\infty$. The compact forms of the Barut-Girardello coherent states corresponding to $l$-representation of $su(1,1)$ algebra and their positive definite measures on the complex plane are also calculated

A fresh look at neutral meson mixing

In this work we show that the existence of a complete biorthonormal set of eigenvectors of the effective Hamiltonian governing the time evolution of neutral meson system is a necessary condition for diagonalizability of such a Hamiltonian. We also study the possibility of probing the $CPT$ invariance by observing the time dependence of cascade decays of type $P^{\circ}(\bar{P^{\circ}})\to \{M_a,M_b\}X\to fX$ by employing such basis and exactly determine the $CPT$ violation parameter by comparing the time dependence of the cascade decays of tagged $P^{\circ}$ and tagged $\bar{P^{\circ}}$.Comment: 11 page

Klauder-Perelomov and Gazeau-Klauder coherent states for an electron in the Morse-like magnetic field

Based on the quantum states of an electron trapped on an infinite band along the x-axis in the presence of the Morse-like perpendicular magnetic field [H. Fakhri, B. Mojaveri, M.A. Gomshi Nobary, Rep. Math. Phys. 66, 299 (2010)], the Klauder-Perelomov and Gazeau-Klauder coherent states are constructed. To realize the resolution of identity, their corresponding positive definite measure on the complex plane are obtained in terms of the known functions. Also, some nonclassical properties such as sub-Poissonian statistics and squeezing effect of constructed coherent states are studied