Algebraic approach to radial ladder operators in the hydrogen atom

Martínez‐y‐Romero, R. P.; Núñez‐Yépez, H. N.; Salas‐Brito, A. L.

doi:10.1002/qua.21317

Cited by 9 publications

(2 citation statements)

References 21 publications

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“…Because of there exist some quantum physical models whose solvability and square integrability are connected with the associated Laguerre polynomials. The Landau levels, Morse potential, Calogero-Sutherland model, half-oscillator, radial part of 3-D harmonic oscillator and radial part of a hydrogen-like atom are the six examples [25][26][27][28][29][30]. They play an important role in the quantum mechanics and have been considered by many authors in the framework of the coherent states theory [25,31,32].…”

Section: Reviews and Motivationmentioning

confidence: 99%

Approach of the Generating Functions to the Coherent States for Some Quantum Solvable Models

Mojaveri¹,

Dehghani²

2014

Preprint

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We introduce to this paper new kinds of coherent states for some quantum solvable models: a free particle on a sphere, one-dimensional Calogero-Sutherland model, the motion of spinless electrons subjected to a perpendicular magnetic field B, respectively , in two dimensional flat surface and an infinite flat band. We explain how these states come directly from the generating functions of the certain families of classical orthogonal polynomials without the complexity of the algebraic approaches. We have shown that some examples become consistent with the Klauder-Perelomove and the Barut-Girardello coherent states. It can be extended to the non-classical, q-orthogonal and the exceptional orthogonal polynomials, too. Especially for physical systems that they don't have a specific algebraic structure or involved with the shape invariance symmetries, too.

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Section: Reviews and Motivationmentioning

confidence: 99%

Approach of the Generating Functions to the Coherent States for Some Quantum Solvable Models

Mojaveri¹,

Dehghani²

2014

Preprint

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“…Note that, the ladder operators can be derived using the algebraic or supersymmetric approaches [6][7][8][9] which have been successfully applied to the Morse, Pöschl-Teller, radial harmonic and other oscillators [10][11][12][13][14][15]. Recently, Dong et al have derived the raising and lowering operators for the Morse [16] and Pöschl-Teller potentials [17] employing some properties of the associated Laguerre and Legandre polynomials.…”

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confidence: 99%

The construction of ladder operators and coherent states for the Wei Hua anharmonic oscillator using the supersymmetric quantum mechanics

et al. 2013

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The unknown ladder operators for the Wei Hua potential have been derived within the algebraic approach. The method is extended to include the rotating oscillator. The annihilation and creation operators have been obtained with the use of the factorization method. The coherent states for the Wei Hua anharmonic oscillator, which are eigenstates of the annihilation operator and minimize the generalized position-momentum uncertainty relation, are constructed in the framework of the supersymmetric quantum mechanics. The constructed ladder operators can be applied to compute the matrix elements in theoretical spectroscopy due to the fact that this potential is widely used to a proper description the large-amplitude vibrations of diatomic molecules.

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

Fakhri

Dehghani

Mojaveri

2009

Int J of Quantum Chemistry

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Using second-order differential operators as a realization of the su(1, 1) Lie algebra by the associated Laguerre functions, it is shown that the quantum states of the Calogero-Sutherland, half-oscillator and radial part of a 3D harmonic oscillator constitute the unitary representations for the same algebra. This su(1, 1) Lie algebra symmetry leads to derivation of the Barut-Girardello and Klauder-Perelomov coherent states for those models. The explicit compact forms of these coherent states are calculated. Also, to realize the resolution of the identity, their corresponding positive definite measures on the complex plane are obtained in terms of the known functions.

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Algebraic approach to radial ladder operators in the hydrogen atom

Cited by 9 publications

References 21 publications

Approach of the Generating Functions to the Coherent States for Some Quantum Solvable Models

Approach of the Generating Functions to the Coherent States for Some Quantum Solvable Models

The construction of ladder operators and coherent states for the Wei Hua anharmonic oscillator using the supersymmetric quantum mechanics

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

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