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Nonclassical properties of a model for modulated damping under the action of an external force

M. Sebawe Abdalla, Lamia E. Thabet, Saudi Arabia, Received Jan, Accepted April

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

We introduce a modified model for the problem of a damped harmonic oscillator in presence of a driving force. The model is treated from the point of view of quantum mechanics. The wave function in the Schr¨ odinger picture is obtained. The connection between the quasicoherent state and pseudostationary state is discussed. The constants of motion are also introduced and the eigenfunctions and the corresponding eigenvalues for pair of quadratic invariants are obtained. The phenomena of squeezing and the Poissonian distribution are considered. It is shown that the system is sensitive to the variation of the damping factor, ∞, as well as of the modulation factor, „.

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We introduce a modified model for the problem of a damped harmonic oscillator in presence of a driving force. The model is treated from the point of view of quantum mechanics. The wave function in the Schr¨ odinger picture is obtained. The connection between the quasicoherent state and pseudostationary state is discussed. The constants of motion are also introduced and the eigenfunctions and the corresponding eigenvalues for pair of quadratic invariants are obtained. The phenomena of squeezing and the Poissonian distribution are considered. It is shown that the system is sensitive to the variation of the damping factor, ∞, as well as of the modulation factor, „.
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.
We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schroedinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator.
We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schroedinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator.
A quantum-mechanical model of a damped harmonic oscillator (both with time-independent and time-dependent parameters) is studied in the framework of the linear Schr\"odinger equation with a Hermitian nonstationary Hamiltonian. Integrals of the motion of this equation and their eigenstates, including coherent states, are constructed. The influence of an external harmonic force to the time evolution of various average values calculated over coherent states is considered, including the resonance case. The specific symmetry of the Hamiltonian leading to the new concept of loss-energy states is discussed.