Related papers: Generalized Coherent States for Classical Orthogon…
In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105], we constructed a class of coherent states for a polynomially deformed $su(2)$ algebra. In this paper, we first prepare the discrete representations of the…
While dealing with a class of generalized Bargmann spaces, we rederive their reproducing kernels from the knowledge of an orthonormal basis by using an addition formula for Laguerre polynomials involving the disk polynomials. We construct…
A linear functional $\bf u$ is classical if there exist polynomials, $\phi$ and $\psi$, with $\deg \phi\le 2$, $\deg \psi=1$, such that ${\mathscr D}\left(\phi(x) {\bf u}\right)=\psi(x){\bf u}$, where ${\mathscr D}$ is a certain…
Two new types of coherent states associated with the C_{\lambda}-extended oscillator, where C_{\lambda} is the cyclic group of order \lambda, are introduced. The first ones include as special cases both the Barut-Girardello and the…
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general…
In this work we describe semiclassical states in graphene under a constant perpendicular magnetic field by constructing coherent states in the Barut-Girardello sense. Since we want to keep track of the angular momentum, the use of the…
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-Schr\"odinger…
Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended…
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
We discuss the construction of oscillator-like systems associated with orthogonal polynomials on the example of the Fibonacci oscillator. In addition, we consider the dimension of the corresponding lie algebras.
Coherent states for power-law potentials are constructed using generalized Heisenberg algabras. Klauder's minimal set of conditions required to obtain coherent states are satisfied. The statistical properties of these states are…
We discuss as a fundamental characteristic of orthogonal polynomials like the existence of a Lie algebra behind them, can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we put…
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general…
States which minimize the Schr\"odinger--Robertson uncertainty relation are constructed as eigenstates of an operator which is a element of the $h(1) \oplus \su(2)$ algebra. The relations with supercoherent and supersqueezed states of the…
A universal disentangling formula (such as the Baker-Campbell-Hausdorff one) for coherent states of Perelomov's type ($ |z \ra = \exp (z\Adag -\bar{z}A) |0 \ra $) which are defined for generalized oscillator algebras is given.
In the frame of our approach we constructed the generalized oscillator connected with Krawtchouk polynomials (named Krawtchouk oscillator) and coherent states for this oscillator too. Ours results are compared with analogues ones obtained…
Multivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the eigenfunctions of certain Schr\"odinger operators for Calogero-Sutherland-type quantum systems. For the generalized…
Orthogonality of the Jacobi and of Laguerre polynomials, P_n^(a,b) and L_n^(a), is established for a,b complex (a,b not negative integers and a+b different from -2,-3,...) using the Hadamard finite part of the integral which gives their…
Using notions of composita and composition of generating functions we obtain explicit formulas for Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated Laguerre polynomials, Stirling polynomials, Abel polynomials,…