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arXiv:quant-ph/9502023

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

Olga V. Man’ko

Published Feb 27, 1995• 0 citations
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Abstract

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.
DOI
10.48550/arxiv.quant-ph/9502023

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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.