Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum oscillator with Kronig-Penney excitation in different regimes of damping

Olga V. Man’ko

Published Feb 27, 1995• 0 citations
OpenAlex

Abstract

There are discussed the exact solution of the time--dependent Schr\\"{o}dinger equation for a damped quantum oscillator subject to a periodical frequency delta--kicks describing squeezed states which are expressed in terms of Chebyshev polynomials. The cases of strong and weak damping are investigated in the frame of Caldirola--Kanai model.

Related papers

Quantum Oscillator with Kronig-Penney Excitation in Different Regimes of Damping

Olga V. Man’ko

There are discussed the exact solution of the time--dependent Schrödinger equation for a damped quantum oscillator subject to a periodical frequency delta--kicks describing squeezed states which are expressed in terms of Chebyshev polynomials. The cases of strong and weak damping are investigated in the frame of Caldirola--Kanai model.

arXiv:quant-ph/9502023•Feb 27, 1995•0 citations

Quantum oscillator with kronig-penney excitation in different regimes of damping

Olga V. Man’ko

The behaviour of an oscillator may be controlled by the frequency time-dependence. For example, one can kick the oscillator frequency by short pulses and this kicking produces an excitation of the parametric oscillator. The amplitude of the oscillator vibrations and its energy may increase due to the external influence expressed as the frequency time-dependence. Also the statistical properties of the oscillator state may be changed due to the action of external forces. The aim of the talk is to discuss the exact solution of the time-dependent Schrodinger equation for a damped quantum oscillator subject to a periodical frequency delta-kicks describing squeezed states which are expressed in terms of Chebyshev polynomials. The cases of strong and weak damping are investigated in the frame of Caldirola-Kanai model [1], [2].

European Quantum Electronics Conference (EQEC)•Aug 24, 2005•0 citations

Damped Oscillator with Delta-Kicked Frequency

Olga V. Man’ko

Exact solutions of the Schrodinger equation for quantum damped oscillator subject to frequency delta-kick describing squeezed states are obtained. The cases of strong, intermediate, and weak damping are investigated.

•Jan 1, 1996•0 citations

Quantum mechanics of the damped pulsating oscillator

M. Sebawe Abdalla, Ursula A.T. Ramjit

A harmonic oscillator subject to the combined effects of damping and pulsating is represented by a Kanai–Caldirola Hamiltonian. The equations of motion are solved in the Heisenberg picture in the case of weak pulsation. The rotating-wave approximation (RWA) is used to obtain the motion in the neighborhood of the principal resonance. The RWA Schrödinger equation is solved exactly and pseudostationary and quasicoherent states are described. The transition probability between quasicoherent and coherent states is obtained and the gain in energy is discussed.

Journal of Mathematical Physics•Jan 1, 1989•19 citations

Quantum Damped Mechanical Oscillator

A. N. Ikot, Louis E. Akpabio, Ita O. Akpan +2 more

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.

International Journal of Optics•Jan 1, 2010•6 citations

Quantum Theory of Damped Harmonic Oscillator

Akaninyene Daniel Antia, Eno E. Ituen, A. N. Ikot +2 more

The exact solutions of the Schrodinger equation for damped harmonic oscillator with pulsating mass and modified Caldirola-Kanai Hamiltonian are evaluated. We also investigated the case of under-damped for the two models constructed and the results obtained in both cases do not violate Heisenberg uncertainty principle.

Global Journal of Pure and Applied Sciences•Jan 1, 2010•3 citations
There are discussed the exact solution of the time--dependent Schr\"{o}dinger equation for a damped quantum oscillator subject to a periodical frequency delta--kicks describing squeezed states which are expressed in terms of Chebyshev polynomials. The cases of strong and weak damping are investigated in the frame of Caldirola--Kanai model.
The behaviour of an oscillator may be controlled by the frequency time-dependence. For example, one can kick the oscillator frequency by short pulses and this kicking produces an excitation of the parametric oscillator. The amplitude of the oscillator vibrations and its energy may increase due to the external influence expressed as the frequency time-dependence. Also the statistical properties of the oscillator state may be changed due to the action of external forces. The aim of the talk is to discuss the exact solution of the time-dependent Schrodinger equation for a damped quantum oscillator subject to a periodical frequency delta-kicks describing squeezed states which are expressed in terms of Chebyshev polynomials. The cases of strong and weak damping are investigated in the frame of Caldirola-Kanai model [1], [2].
A harmonic oscillator subject to the combined effects of damping and pulsating is represented by a Kanai–Caldirola Hamiltonian. The equations of motion are solved in the Heisenberg picture in the case of weak pulsation. The rotating-wave approximation (RWA) is used to obtain the motion in the neighborhood of the principal resonance. The RWA Schrödinger equation is solved exactly and pseudostationary and quasicoherent states are described. The transition probability between quasicoherent and coherent states is obtained and the gain in energy is discussed.