scholarly journals Phase coherent states with circular Jacobi polynomials for the pseudoharmonic oscillator

2012 ◽  
Vol 53 (1) ◽  
pp. 012103 ◽  
Author(s):  
Zouhaïr Mouayn
Keyword(s):  
Coherent States ◽  
Jacobi Polynomials ◽  
Pseudoharmonic Oscillator

scholarly journals COMPLEXIFIER VERSUS FACTORIZATION AND DEFORMATION METHODS FOR GENERATION OF COHERENT STATES OF A 1D NLHO I: MATHEMATICAL CONSTRUCTION

2013 ◽  
Vol 10 (10) ◽  
pp. 1350056 ◽  
Author(s):  
R. ROKNIZADEH ◽  
H. HEYDARI
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
One Dimensional ◽  
The Difference ◽  
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 [Formula: see text], bridging the difference between them is possible, we give here also the exact solution of Schrödinger equation of 1D NLHO in terms of Jacobi polynomials.

Excitation on the Coherent States of Pseudoharmonic Oscillator

2009 ◽  
Author(s):  
Dusan Popov ◽  
Nicolina Pop ◽  
Vjekoslav Sajfert ◽  
Madalin Bunoiu ◽  
Iosif Malaescu
Keyword(s):  
Coherent States ◽  
Pseudoharmonic Oscillator

A new generalization of nonlinear coherent states for the pseudoharmonic oscillator

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
K. Ahbli ◽  
H. Kassogué ◽  
P. Kayupe Kikodio ◽  
A. Kouraich
Keyword(s):  
Coherent States ◽  
Pseudoharmonic Oscillator

Pseudoharmonic oscillator and their associated Gazeau–Klauder coherent states

2008 ◽  
Vol 387 (16-17) ◽  
pp. 4459-4474 ◽  
Author(s):  
Dušan Popov ◽  
Vjekoslav Sajfert ◽  
Ioan Zaharie
Keyword(s):  
Coherent States ◽  
Pseudoharmonic Oscillator

Coherent states attached to the quantum disc algebra and their associated polynomials

2021 ◽  
pp. 2150078
Author(s):  
H. Fakhri ◽  
M. Refahinozhat
Keyword(s):  
Coherent States ◽  
Jacobi Polynomials ◽  
Hermite Polynomials ◽  
Hermitian Operator ◽  
Fock Representation ◽  
Disc Algebra ◽  
Variable Formula ◽  
Associated Polynomials ◽  
Hermitian Conjugate ◽  
The One

The one-variable [Formula: see text]-coherent states attached to the [Formula: see text]-disc algebra are constructed and used to obtain the [Formula: see text]-Bargmann–Fock realization of its Fock representation. Then, this realization is used to obtain the [Formula: see text]-continuous Hermite polynomials as well as continuous and discrete [Formula: see text]-Hermite polynomials by using a pair of Hermitian canonical conjugate operators and two pairs of the non-Hermitian conjugate operators, respectively. Besides, we introduce a two-variable family of [Formula: see text]-coherent states attached to the Fock representation space of the [Formula: see text]-disc algebra and its opposite algebra and obtain their simultaneous [Formula: see text]-Bargmann–Fock realization. For an appropriate non-Hermitian operator, the latter realization is served to obtain the well-known little [Formula: see text]-Jacobi polynomials used in constructing the [Formula: see text]-disc polynomials.

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