Quantum Damped Mechanical Oscillator

Ikot, Akpan N.; Akpabio, Louis E.; Akpan, I. O.; Umo, M. I.; Ituen, Eno E.

doi:10.1155/2010/275910

Cited by 7 publications

(5 citation statements)

References 26 publications

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“…When b → 0 and μ ( t ) → μ 0 (constant), our model recovers to that of the standard CK oscillator, whereas, in the case that a → 0, it becomes a somewhat different model of a modified CK oscillator given in Ref. 51 .…”

Section: Discussionmentioning

confidence: 58%

A novel method for analyzing complicated quantum behaviors of light waves in oscillating turbulent plasma

Choi

2014

Sci Rep

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Quantum dynamics of light waves traveling through a time-varying turbulent plasma is investigated via the SU(1,1) Lie algebraic approach. Plasma oscillations that accompany time-dependence of electromagnetic parameters of the plasma are considered. In particular, we assume that the conductivity of plasma involves a sinusoidally varying term in addition to a constant one. Regarding the time behavior of electromagnetic parameters in media, the light fields are modeled as a modified CK (Caldirola-Kanai) oscillator that is more complex than the standard CK oscillator. Diverse quantum properties of the system are analyzed under the consideration of time-dependent characteristics of electromagnetic parameters. Quantum energy of the light waves is derived and compared with the counterpart classical energy. Gaussian wave packet of the field whose probability density oscillates with time like that of classical states is constructed through a choice of suitable initial condition and its quantum behavior is investigated in detail. Our development presented here provides a useful way for analyzing time behavior of quantized light in complex plasma.

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Section: Discussionmentioning

confidence: 58%

A novel method for analyzing complicated quantum behaviors of light waves in oscillating turbulent plasma

Choi

2014

Sci Rep

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“…Let us illustrate quantum Lie systems through an example. Consider the quantum one-dimensional Caldirola-Kanai oscillator [43][44][45][46], which is determined by the t-dependent operator…”

Section: Quantum Lie Systemsmentioning

confidence: 99%

Quantum quasi-Lie systems: properties and applications

2023

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A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a t-dependent vector field that is equivalent to a t-dependent family of vector fields within a finite-dimensional Lie algebra of vector fields. Lie systems have been generalised in the literature to deal with t-dependent Schrödinger equations determined by a particular class of t-dependent Hamiltonian operators, the quantum Lie systems, and other systems of differential equations through the so-called quasi-Lie schemes. This work extends quasi-Lie schemes and quantum Lie systems to cope with t-dependent Schrödinger equations associated with the here-called quantum quasi-Lie systems. To illustrate our methods, we propose and study a quantum analogue of the classical nonlinear oscillator searched by Perelomov, and we analyse a quantum one-dimensional fluid in a trapping potential along with quantum t-dependent Smorodinsky–Winternitz oscillators.

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“…Let us illustrate quantum Lie systems through an example. Consider the quantum onedimensional Caldirola-Kanai oscillator [4,9,42,43], which is determined by the t-dependent operator…”

Section: Quantum Lie Systemsmentioning

confidence: 99%

Quantum quasi-Lie systems: properties and applications

Cariñena¹,

Lucas²,

Sardón³

2022

Preprint

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A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional Lie algebra of vector fields. Lie systems have been generalised in the literature to deal with t-dependent Schrödinger equations determined by a particular class of t-dependent Hamiltonian operators, the quantum Lie systems, and other differential equations through the so-called quasi-Lie schemes. This work extends quasi-Lie schemes and quantum Lie systems to cope with tdependent Schrödinger equations associated with the here called quantum quasi-Lie systems. To illustrate our methods, we propose and study a quantum analogue of the classical nonlinear oscillator searched by Perelomov and we analyse a quantum one-dimensional fluid in a trapping potential along with quantum t-dependent Smorodinsky-Winternitz oscillators.

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Quantum Damped Mechanical Oscillator

Abstract: The exact solutions of the Schrödinger equation for quantum damped oscillator with modified Caldirola-Kanai Hamiltonian are evaluated. We also investigate the cases of under-, over-, and critical damping.

Cited by 7 publications

References 26 publications

A novel method for analyzing complicated quantum behaviors of light waves in oscillating turbulent plasma

A novel method for analyzing complicated quantum behaviors of light waves in oscillating turbulent plasma

Quantum quasi-Lie systems: properties and applications

Quantum quasi-Lie systems: properties and applications

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