Representation of the q-Deformed Oscillator

2000 ◽  
pp. 97-99
Author(s):  
Alain Guichardet
Keyword(s):  
Deformed Oscillator

scholarly journals Symmetries and integrals of motion of a superintegrable deformed oscillator

2021 ◽  
pp. 168428
Author(s):  
Joanna Gonera ◽  
Artur Jasiński ◽  
Piotr Kosiński
Keyword(s):  
Integrals Of Motion ◽  
Deformed Oscillator

Algebraic approach to the projected deformed oscillator model

1981 ◽  
Vol 355 (1) ◽  
pp. 25-44 ◽  
Author(s):  
R.M. Asherova ◽  
Yu.F. Smirnov ◽  
V.N. Tolstoy ◽  
A.P. Shustov
Keyword(s):  
Algebraic Approach ◽  
Oscillator Model ◽  
Deformed Oscillator

Deformed oscillator for the Morse potential

1993 ◽  
Vol 203 (2-3) ◽  
pp. 150-156 ◽  
Author(s):  
Dennis Bonatsos ◽  
C. Daskaloyannis
Keyword(s):  
Morse Potential ◽  
Deformed Oscillator

Photon added coherent states of the parity deformed oscillator

2019 ◽  
Vol 34 (14) ◽  
pp. 1950104 ◽  
Author(s):  
A. Dehghani ◽  
B. Mojaveri ◽  
S. Amiri Faseghandis
Keyword(s):  
Coherent States ◽  
Uncertainty Relation ◽  
Annihilation Operator ◽  
Single Mode ◽  
Heisenberg Algebra ◽  
Uncertainty Relations ◽  
Deformed Oscillator ◽  
Cat States ◽  
Poissonian Statistics ◽  
Creation Operators

Using the parity deformed Heisenberg algebra (RDHA), we first establish associated coherent states (RDCSs) for a pseudo-harmonic oscillator (PHO) system that are defined as eigenstates of a deformed annihilation operator. Such states can be expressed as superposition of an even and odd Wigner cat states.[Formula: see text] The RDCSs minimize a corresponding uncertainty relation, and resolve an identity condition through a positive definite measure which is explicitly derived. We introduce a class of single-mode excited coherent states (PARDCS) of the PHO through “m” times application of deformed creation operators to RDCS. For the states thus constructed, we analyze their statistical properties such as squeezing and sub-Poissonian statistics as well as their uncertainty relations.

scholarly journals COHERENT STATES, DISPLACED NUMBER STATES AND LAGUERRE POLYNOMIAL STATES FOR su(1, 1) LIE ALGEBRA

2000 ◽  
Vol 14 (10) ◽  
pp. 1093-1103 ◽  
Author(s):  
XIAO-GUANG WANG
Keyword(s):  
Coherent State ◽  
Lie Algebra ◽  
Hypergeometric Functions ◽  
Laguerre Polynomial ◽  
Optical Systems ◽  
Matrix Elements ◽  
Operator Formalism ◽  
Ladder Operator ◽  
Deformed Oscillator ◽  
The Matrix

The ladder operator formalism of a general quantum state for su(1, 1) Lie algebra is obtained. The state bears the generally deformed oscillator algebraic structure. It is found that the Perelomov's coherent state is a su(1, 1) nonlinear coherent state. The expansion and the exponential form of the nonlinear coherent state are given. We obtain the matrix elements of the su(1, 1) displacement operator in terms of the hypergeometric functions and the expansions of the displaced number states and Laguerre polynomial states are followed. Finally some interesting su(1, 1) optical systems are discussed.

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