Klauder–perelomov and Gazeau–klauder Coherent States for Some Shape Invariant Potentials

Chenaghlou, A.; Fakhri, H.

doi:10.1142/s0217732302008095

Cited by 28 publications

(22 citation statements)

References 26 publications

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“…The ladder operators can be constructed using the algebraic or supersymmetric (SUSY) approaches [4,5] which have been successfully applied to the Morse, Pöschl-Teller, radial harmonic and other oscillators [6][7][8][9][10][11][12][13][14][15]. The fundamental study in this direction was developed by Schrödinger [16], who introduced the factorization method into quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

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The algebraic approach for the derivation of ladder operators and coherent states for the Goldman and Krivchenkov oscillator by the use of supersymmetric quantum mechanics

Mikulski

Eder²,

Molski

2014

J Math Chem

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The ladder operators for the Goldman and Krivchenkov anharmonic potential have been derived within the algebraic approach. The method is extended to include the rotating oscillator. The coherent states for the Goldman and Krivchenkov oscillator, which are the eigenstates of the annihilation operator and minimize the generalized position-momentum uncertainty relation, are constructed within the framework of supersymmetric quantum mechanics. The constructed ladder operators can be a useful tool in quantum chemistry computations of non-trivial matrix elements. In particular, they can be employed in molecular vibrational-rotational spectroscopy of diatomic molecules to compute transition energies and dipole matrix elements.

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Section: Introductionmentioning

confidence: 99%

“…Adopting this approach Popov [33] obtained Barut-Girardello coherent states for the Morse potential. Chenaghou and Fakhri [10] derived these coherent states for the Eckart and RosenMorse potentials.…”

Section: Introductionmentioning

confidence: 99%

The algebraic approach for the derivation of ladder operators and coherent states for the Goldman and Krivchenkov oscillator by the use of supersymmetric quantum mechanics

Mikulski

Eder²,

Molski

2014

J Math Chem

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“…In recent years, many authors have investigated new quantum states of the electromagnetic field such as coherent states [1][2][3][4][5][6][7][8][9][10][11][12] which provide us with a link between quantum and classical mechanics and nowadays pervade many branches of physics including quantum electrodynamics, solid-state physics, and nuclear and atomic physics, from both theoretical and experimental viewpoints. In addition to CSs, squeezed states (SSs) are becoming increasingly important.…”

Section: Introductionmentioning

confidence: 99%

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

Dehghani

2014

Journal of Mathematical Physics

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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.

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“…These efforts have been started by Schrödinger [2] and followed by others who were interested in finding quantum mechanical states which provide a close connection between classical and quantum formulations of a given physical system in the context of the coherent states [3][4][5][6][7][8][9][10][11]. These states can also be generated using algebraic methods [12], supersymmetric quantum mechanics [13,14] and its application to different physical situations [15][16][17][18][19][20][21][22][23][24]. In this paper, we pursue a different approach to construct wave packets with complete classical and quantum correspondence.…”

Section: Introductionmentioning

confidence: 99%

An Approach to Construct Wave Packets with Complete Classical-Quantum Correspondence in Non-relativistic Quantum Mechanics

Pedram

2009

Int J Theor Phys

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We introduce a method to construct wave packets with complete classical and quantum correspondence in one-dimensional non-relativistic quantum mechanics. First, we consider two similar oscillators with equal total energy. In classical domain, we can easily solve this model and obtain the trajectories in the space of variables. This picture in the quantum level is equivalent with a hyperbolic partial differential equation which gives us a freedom for choosing the initial wave function and its initial slope. By taking advantage of this freedom, we propose a method to choose an appropriate initial condition which is independent from the form of the oscillators. We then construct the wave packets for some cases and show that these wave packets closely follow the whole classical trajectories and peak on them. Moreover, we use de-Broglie Bohm interpretation of quantum mechanics to quantify this correspondence and show that the resulting Bohmian trajectories are also in complete agreement with their classical counterparts.

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Klauder–perelomov and Gazeau–klauder Coherent States for Some Shape Invariant Potentials

Cited by 28 publications

References 26 publications

The algebraic approach for the derivation of ladder operators and coherent states for the Goldman and Krivchenkov oscillator by the use of supersymmetric quantum mechanics

The algebraic approach for the derivation of ladder operators and coherent states for the Goldman and Krivchenkov oscillator by the use of supersymmetric quantum mechanics

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

An Approach to Construct Wave Packets with Complete Classical-Quantum Correspondence in Non-relativistic Quantum Mechanics

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