Superrevivals in the quantum dynamics of a particle confined in a finite square-well potential

Venugopalan, Anu; Agarwal, G. S.

doi:10.1103/physreva.59.1413

Cited by 33 publications

(18 citation statements)

References 27 publications

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“…Let us remind that the quantity k 0 defined in (3) cannot be obtained putting n = 0 in (29), (31), (32).…”

Section: The Quantum Square Wellmentioning

confidence: 99%

Square wells, quantum wells and ultra-thin metallic films

Barsan

2013

Philosophical Magazine

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The eigenvalue equations for the energy of bound states of a particle in a square well are solved, and the exact solutions are obtained, as power series. Accurate analytical approximate solutions are also given. The application of these results in the physics of quantum wells are discussed,especially for ultra-thin metallic films, but also in the case of resonant cavities, heterojunction lasers, revivals and super-revivals.

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“…Let us remind that the quantity k 0 defined in (3) cannot be obtained putting n = 0 in (29), (31), (32).…”

Section: The Quantum Square Wellmentioning

confidence: 99%

Square wells, quantum wells and ultra-thin metallic films

Barsan

2013

Philosophical Magazine

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“…Venugopalan and Agarwal 26 recently presented a numerical study of dynamics in finite square wells. With the expressions for the time scales, Eqs.…”

Section: B Example Of Wave-packet Dynamicsmentioning

confidence: 99%

General series solution for finite square-well energy levels for use in wave-packet studies

Aronstein

Stroud

2000

American Journal of Physics

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We develop a series solution for the bound-state energy levels of the quantum-mechanical one-dimensional finite square-well potential. We show that this general solution is useful for local approximations of the energy spectrum ͑which target a particular energy range of the potential well for high accuracy͒, for global approximations of the energy spectrum ͑which provide analytic expressions of reasonable accuracy for the entire range of bound states͒, and for numerical methods. This solution also provides an analytic description of dynamical phenomena; with it, we compute the time scales of classical motion, revivals, and super-revivals for wave-packet states excited in the well.

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“…The second kind of equation is where   p p p n x n 2 2 2.This equation comes from the problem of a particle moving in a finite square well potential where the energy eigenvalues are its roots [4]. After the fabrication of quantum wells [5], the experimental observation of revivals and super-revivals [6] and the progress of the so-called 'ghost orbit spectroscopy' [7], the square wells also describe realistic physical systems or phenomena. The need for an explicit solution exceeds the level of solving simple and relevant problems of quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Approximate expressions for solutions to two kinds of transcendental equations with applications

Liu

Yang

et al. 2018

J. Phys. Commun.

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In a broad spectrum of physics and engineering applications, transcendental equations have to be solved in order to determine their roots. Exact and explicit algebraic expression of solutions to such equations is, in general, impossible. Analytical approximate solutions to two kinds of transcendental equations with wide applications are presented. These approximate root formulas are systematically established by using the Padé approximant and show high accuracy. As an application of the proposed approximations, a highly accurate expression of the effective mass of the spring for a spring-mass system is obtained. The method described in this paper is also applied to other transcendental equations in physics and engineering applications.

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Superrevivals in the quantum dynamics of a particle confined in a finite square-well potential

Cited by 33 publications

References 27 publications

Square wells, quantum wells and ultra-thin metallic films

Square wells, quantum wells and ultra-thin metallic films

General series solution for finite square-well energy levels for use in wave-packet studies

Approximate expressions for solutions to two kinds of transcendental equations with applications

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