Time behavior of a Gaussian wave packet accompanying the generalized coherent state for the inverted oscillator

Maamache, M.; Bouguerra, Yacine; Choi, Jeong Ryeol

doi:10.1093/ptep/ptw057

Cited by 8 publications

(10 citation statements)

References 25 publications

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“…We start with the 1-D Schrodinger equation for the inverted harmonic potential. (i.e., the harmonic force is repulsive rather than attractive [30][31][32][33][34][35]). The equation reads…”

Section: Parabolic Cylinder Wavesmentioning

confidence: 99%

Self-accelerating parabolic cylinder waves in 1-D

Yüce¹

2016

Physics Letters A

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“…We start with the 1-D Schrodinger equation for the inverted harmonic potential. (i.e., the harmonic force is repulsive rather than attractive [30][31][32][33][34][35]). The equation reads…”

Section: Parabolic Cylinder Wavesmentioning

confidence: 99%

Self-accelerating parabolic cylinder waves in 1-D

Yüce¹

2016

Physics Letters A

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“…From the illustration of the corresponding probability densities, the time behavior of the system will be analyzed. The properties of the wave packet obtained in this work will also be compared to the previously known localized Gaussian wave packet [28]. Eventually, we will discuss the correspondence between quantum and classical mechanics of the system.…”

Section: Introductionmentioning

confidence: 85%

“…For this purpose, an elegant exact theory associated with the quantum description of the system is important. The invariant operator method, which was developed by Lewis and Riesenfeld [26,27], will be used here to investigate the quantum characteristics of the inverted oscillator [28][29][30]. A quantum wave packet of the system, represented in terms of an Airy function, will be developed by means of a linear invariant operator.…”

Section: Introductionmentioning

confidence: 99%

Quantum-classical correspondence for the inverted oscillator

Maamache

Choi

2017

Chinese Phys. C

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While quantum-classical correspondence for a system is a very fundamental problem in modern physics, the understanding of its mechanism is often elusive, so the methods used and the results of detailed theoretical analysis have been accompanied by active debate. In this study, the differences and similarities between quantum and classical behavior for an inverted oscillator have been analyzed based on the description of a complete generalized Airy function-type quantum wave solution. The inverted oscillator model plays an important role in several branches of cosmology and particle physics. The quantum wave packet of the system is composed of many sub-packets that are localized at different positions with regular intervals between them. It is shown from illustrations of the probability density that, although the quantum trajectory of the wave propagation is somewhat different from the corresponding classical one, the difference becomes relatively small when the classical excitation is sufficiently high. We have confirmed that a quantum wave packet moving along a positive or negative direction accelerates over time like a classical wave. From these main interpretations and others in the text, we conclude that our theory exquisitely illustrates quantum and classical correspondence for the system, which is a crucial concept in quantum mechanics.

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“…The Hamiltonian ( 12) is formally obtainable from ( 5) by the replacement ω → iω, (13) similarly, the case (−iω) would serve equally well. On the other hand, for an imaginary frequency, i.e.…”

Section: Summary Of Standard Harmonic and The Inverted Oscillatorsmentioning

confidence: 99%

“…The inverted oscillator, equipped with a potential exerting a repulsive force on a particle, has been widely studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Such system can be completely solved as the standard harmonic oscillator whose properties are well known.…”

Section: Introductionmentioning

confidence: 99%

Inverted oscillator: pseudo hermiticity and coherent states

Zerimeche¹,

Moufok²,

Amaouche³

et al. 2023

Rev. Mex. Fís.

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It is known that the standard and the inverted harmonic oscillator are different. Replacing thus ω by ±iω in the regular oscillator is necessary going to give the inverted oscillator H^{r}. This replacement would lead to anti- PT-symmetric harmonic oscillator Hamiltonian (∓iH^{os}). The pseudo-hermiticity relation has been used here to relate the anti-PT-symmetric harmonic Hamiltonian to the inverted oscillator. By using a simple algebra, we introduce the ladder operators describing the inverted harmonic oscillator to reproduce the analytical solutions.We construct the inverted coherent states which minimize the quantum mechanical uncertainty between the position and the momentum. This paper is dedicated to the memory of Omar Djemli and Nouredinne Mebarki who died due to covid 19.

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Time behavior of a Gaussian wave packet accompanying the generalized coherent state for the inverted oscillator

Cited by 8 publications

References 25 publications

Self-accelerating parabolic cylinder waves in 1-D

Self-accelerating parabolic cylinder waves in 1-D

Quantum-classical correspondence for the inverted oscillator

Inverted oscillator: pseudo hermiticity and coherent states

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