Approach of the associated Laguerre functions to the <i>su</i>(1,1) coherent states for some quantum solvable models

Fakhri, H.; Dehghani, A.; Mojaveri, B.

doi:10.1002/qua.21944

Cited by 18 publications

(16 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the literature, various coherent states [58][59][60] are contructed for different Lie algebra. To construct the appropriate coherent states for this system whose eigenfunction is expressed in terms of the generalized Laguerre functions as in [61][62][63][64][65][66], we factorise this eigenfunction to find the hidden symmetry of the system through the establishment of an appropriate Lie algebra.…”

Section: Heisenberg's Uncertainty Relationsmentioning

confidence: 99%

Lewis-Riesenfeld quantization and SU(1, 1) coherent states for 2D damped harmonic oscillator

Lawson

Avossevou

Gouba

2018

Journal of Mathematical Physics

View full text Add to dashboard Cite

In this paper we study a two-dimensional [2D] rotationally symmetric harmonic oscillator with time-dependent frictional force. At the classical level, we solve the equations of motion for a particular case of the time-dependent coefficient of friction. At the quantum level, we use the Lewis-Riesenfeld procedure of invariants to construct exact solutions for the corresponding timedependent Schrödinger equations. The eigenfunctions obtained are in terms of the generalized Laguerre polynomials. By mean of the solutions we verify a generalization version of the Heisenberg's uncertainty relation and derive the generators of the su(1, 1) Lie algebra. Based on these generators, we construct the coherent statesà la Barut-Girardello andà la Perelomov and respectively study their properties. *

show abstract

Section: Heisenberg's Uncertainty Relationsmentioning

confidence: 99%

Lewis-Riesenfeld quantization and SU(1, 1) coherent states for 2D damped harmonic oscillator

Lawson

Avossevou

Gouba

2018

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…PHO may be more suitable model for the description of vibrating molecules. For this reason, the study of CSs for PHO is of great importance which has recently been studied Klauder-Perelomov and Barut-Girardello type CSs in the framework of su(1, 1) Lie algebra symmetry [44,45,46]. The aim of this work is introducing a new approach to construct GCSs for PHO.…”

Section: Introductionmentioning

confidence: 99%

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

Mojaveri

Dehghani

2013

Eur. Phys. J. D

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…For instance, the explicit compact forms of |z, f 0 λ reduces to the standard Barut-Girardello coherent states [33] x|z, f 0 λ = √ 2x − z |z|…”

Section: ♦ Time Evolutionmentioning

confidence: 99%

“…In order to justify the effectiveness of this technique, wide range of non-classical quantum states associated to Lie group SU(1, 1) and corresponding with the Calogero-Sutherland model will be constructed. Because of the two-particle Calogero-Sutherland model has attracted considerable interests [31,32,33] and enjoys the su(1, 1) dynamic symmetry [34,35], too. It is of great interest in quantum optics because it can characterize many kinds of quantum optical systems [7,8,36].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

General displaced SU(1, 1) number states: Revisited

Dehghani

2014

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

The most general displaced number states, based on the bosonic and an irreducible representation( IREP) of the Lie algebra symmetry of su(1, 1) and associated to the Calogero-Sutherland model are introduced. Here, we utilize the Barut-Girardello displacement operator instead of the Klauder-Perelomov counterpart, to construct new kind of the displaced number states which can be classified in nonlinear coherent states regime, too, with special nonlinearity functions. They depend on two parameters, and can be converted into the well known Barut-Girardello coherent and number states respectively, depending on which of the parameters equal to zero. A discussion of the statistical properties of these states is included. Significant are their squeezing properties and anti bunching effects which can be raised by increasing the energy quantum number. Depending on the particular choice of the parameters of the above scenario, we are able to determine the status of compliance with flexible statistics. Major parts of the issue is spent on something that these states, in fact, should be considered as new kind of photon-added coherent states, too. Which can be reproduced through an iterated action of a creation operator on new nonlinear Barut-Girardello coherent states. Where the latter carry, also, outstanding statistical features.

show abstract

Approach of the associated Laguerre functions to the su(1,1) coherent states for some quantum solvable models

Cited by 18 publications

References 29 publications

Lewis-Riesenfeld quantization and SU(1, 1) coherent states for 2D damped harmonic oscillator

Lewis-Riesenfeld quantization and SU(1, 1) coherent states for 2D damped harmonic oscillator

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

General displaced SU(1, 1) number states: Revisited

Contact Info

Product

Resources

About