Quasi-coherent states for damped and forced harmonic oscillator

Dernek, Mustafa; Ünal, Necmettin

doi:10.1063/1.4819261

Cited by 3 publications

(4 citation statements)

References 35 publications

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“…with ḟ = df dt , and η = η(t) a complex-valued function that arises by integration. The introduction of ( 15) into (12) gives the energy potential…”

Section: Point Transformationsmentioning

confidence: 99%

“…The detailed derivation of equations (11)- (12) in terms of point transformations [55] is as follows. We first consider the explicit dependence of X, τ, and ψ on the set y x t x t , ; , { ( )} given in (8)- (9).…”

Section: Appendix a Point Transformationmentioning

confidence: 99%

“…The dynamics of many physical systems is described by using quantum time-dependent harmonic oscillators [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], where the construction of minimum wave packets is relevant [20][21][22][23][24][25][26][27][28][29][30] (see also the recent reviews [31,32]). Such a diversity of applications is due to the quadratic profile of the oscillator [7,[33][34][35][36][37][38][39][40], which is also useful in the trapping of quantum particles with electromagnetic fields [2,3,6,9,10,27,28,[41]…”

Section: Introductionmentioning

confidence: 99%

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Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations

Zelaya

Rosas-Ortiz

2020

Phys. Scr.

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We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with timedependent frequencies that are subjected to the action of a time-dependent driving force, and have a time-dependent zero point energy. Our approach uses the method of point transformations to construct the physical solutions of the parametric oscillator as mere deformations of the well known solutions of the stationary oscillator. In this form, the determination of the quantum integrals of motion is automatically achieved as a natural consequence of the transformation, without necessity of any ansätz. It yields the mechanism to construct an orthonormal basis for the nonstationary oscillators, so arbitrary superpositions of orthogonal states are available to obtain the corresponding coherent states. We also show that the dynamical algebra of the parametric oscillator is immediately obtained as a deformation of the algebra generated by the conventional boson ladder operators. A number of explicit examples is provided to show the applicability of our approach.

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“…with ḟ = df dt , and η = η(t) a complex-valued function that arises by integration. The introduction of ( 15) into (12) gives the energy potential…”

Section: Point Transformationsmentioning

confidence: 99%

Section: Appendix a Point Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations

Zelaya

Rosas-Ortiz

2020

Phys. Scr.

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“…For this particular case, a constant frequency ω 2 (t) = w 2 1 and a driven force F (t) = A 0 cos(νt), for ν, A 0 ∈ R, are considered. This leads to a forced Caldirola-Kanai oscillator Hamiltonian [10,44] of the form…”

Section: Caldirola-kanai Casementioning

confidence: 99%

Time-dependent mass oscillators: constants of motion and semiclasical states

Zelaya

2022

Acta Polytech

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This work reports the construction of constants of motion for a family of time-dependent mass oscillators, achieved by implementing the formalism of form-preserving point transformations. The latter allows obtaining a spectral problem for each constant of motion, one of which leads to a non-orthogonal set of eigensolutions that are, in turn, coherent states. That is, eigensolutions whose wavepacket follows a classical trajectory and saturate, in this case, the Schrödinger-Robertson uncertainty relationship. Results obtained in this form are relatively general, and some particular examples are considered to illustrate the results further. Notably, a regularized Caldirola-Kanai mass term is introduced in an attempt to amend some of the unusual features found in the conventionalCaldirola-Kanai case.

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Quasi-coherent states for the Hermite oscillator

Ünal

2018

Journal of Mathematical Physics

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In this study, we obtained the quasi-coherent states of the damped harmonic oscillator which satisfy the Hermite differential equation classically. For the general damped oscillator, the Gaussian wave packets were derived in configuration and momentum spaces with minimum uncertainities at t = 0, and the quasi-stationary states also obtained and showed that the expansion coefficients give a time-dependent Poisson distribution. As a special case, we found the displaced Gaussian wave packets for the Hermite oscillator and also discussed the weak coupling limit of the wave packets.

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Quasi-coherent states for damped and forced harmonic oscillator

Cited by 3 publications

References 35 publications

Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations

Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations

Time-dependent mass oscillators: constants of motion and semiclasical states

Quasi-coherent states for the Hermite oscillator

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