Non-linear coherent states associated with conditionally exactly solvable problems

Junker, Georg; Roy, Provas Kumar

doi:10.1016/s0375-9601(99)00317-5

Cited by 37 publications

(26 citation statements)

References 20 publications

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“…For such a purpose, we will interpret the latter as an inverse Mellin transform problem [42], as done in related contexts before [23,26,33,34,43,44], by setting for complex s, k → s − 1 and rewriting (4.4) as…”

Section: Unity Resolution Relationsmentioning

confidence: 99%

“…For r > 0 and α = 0, it is known [23,26,33] that Eq. (4.7) has a positive solution in terms of a Meijer G-function [45],…”

Section: Unity Resolution Relationsmentioning

confidence: 99%

“…It should be noted that the algebra (1.2) may also be seen as a deformed su(1,1) algebra. Hence the eigenstates of a may be considered as a deformation of the Barut-Girardello su(1,1) CS [26].…”

Section: Introductionmentioning

confidence: 99%

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Generalized Coherent States Associated with the Cλ-Extended Oscillator

Quesne¹

2001

Annals of Physics

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Two new types of coherent states associated with the C λ -extended oscillator, where C λ is the cyclic group of order λ, are introduced. The first ones include as special cases both the Barut-Girardello and the Perelomov su(1,1) coherent states for λ = 2, as well as the annihilation-operator coherent states of the C λ -extended oscillator spectrum generating algebra for higher λ values. The second ones, which are eigenstates of the C λ -extended oscillator annihilation operator, extend to higher λ values the paraboson coherent states, to which they reduce for λ = 2. All these states satisfy a unity resolution relation in the C λ -extended oscillator Fock space (or in some subspace thereof). They give rise to Bargmann representations of the latter, wherein the generators of the C λ -extended oscillator algebra are realized as differential-operatorvalued matrices (or differential operators). The statistical and squeezing properties of the new coherent states are investigated over a wide range of parameters and some interesting nonclassical features are exhibited.

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Section: Unity Resolution Relationsmentioning

confidence: 99%

“…For r > 0 and α = 0, it is known [23,26,33] that Eq. (4.7) has a positive solution in terms of a Meijer G-function [45],…”

Section: Unity Resolution Relationsmentioning

confidence: 99%

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Generalized Coherent States Associated with the Cλ-Extended Oscillator

Quesne¹

2001

Annals of Physics

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“…Therefore, considerable attention has been given to the construction of coherent states for some polynomial algebras. [14][15][16] Specifically, in Ref. 15, Cannata, Junker, and Trost constructed coherent states for the quadratic su(1, 1) algebra stemming from super-symmetric quantum mechanics by demanding them to be eigenstates of the noncompact operator in much the same way that Barut and Girardello 17 constructed the su(1, 1) coherent states.…”

Section: Introductionmentioning

confidence: 99%

Construction of the Barut-Girardello type of coherent states for Pöschl-Teller potential

Zhang¹,

Jiang²,

Guo³

2014

Journal of Mathematical Physics

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The Pöschl-Teller (PT) potential occupies a privileged place among the anharmonic oscillator potentials due to its applications from quantum mechanics to diatomic molecules. For this potential, a polynomial su(1, 1) algebra has been constructed previously. So far, the coherent states (CSs) associated with this algebra have never appeared. In this paper, we construct the coherent states of the Barut-Girardello coherent states (BG-CSs) type for the PT potentials, which have received less attention in the scientific literature. We obtain these CSs and demonstrate that they fulfil all conditions required by the coherent state. The Mandel parameter for the pure BG-CSs and Husimi's and P-quasi distributions (for the mixed-thermal states) is also presented. Finally, the exponential form of the BG-CSs for the PT potential has been presented and enabled us to build Perelomov type CSs for the PT potential. We point out that the BG-CSs and the Perelomov type coherent states (PCSs) are related via Laplace transform. C 2014 AIP Publishing LLC.

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“…Although the original coherent states are introduced in harmonic oscillator system, the application of the coherent states is extended to wide range of physical systems, for instance, those which are described by SU(1, 1), SO (2,1), and SU(2) Lie algebraic groups [6,7,12] or even nonlinear algebraic groups [13]. It is clear that the Lie algebraic approach is a powerful tool in investigating the quantum properties of dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

SU(1,1) Coherent States for the Generalized Two-Mode Time-Dependent Quadratic Hamiltonian System

Choi

Yeon

2007

Int J Theor Phys

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The SU(1, 1) coherent states, so-called Barut-Girardello coherent state and Perelomov coherent state, for the generalized two-mode time-dependent quadratic Hamiltonian system are investigated through SU(1, 1) Lie algebraic formulation. Two-mode Schrödinger cat states defined as an eigenstate ofK 2 − are also studied. We applied our development to two-mode Caldirola-Kanai oscillator which is a typical example of the time-dependent quadratic Hamiltonian system. The time evolution of the quadrature distribution for the probability density in the coherent states are analyzed for the two-mode Caldirola-Kanai oscillator by plotting relevant figures.

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Non-linear coherent states associated with conditionally exactly solvable problems

Cited by 37 publications

References 20 publications

Generalized Coherent States Associated with the Cλ-Extended Oscillator

Generalized Coherent States Associated with the Cλ-Extended Oscillator

Construction of the Barut-Girardello type of coherent states for Pöschl-Teller potential

SU(1,1) Coherent States for the Generalized Two-Mode Time-Dependent Quadratic Hamiltonian System

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