Journal ArticleDOI
Harmonic oscillator with strongly pulsating mass
R K Colegrave,M. Sebawe Abdalla +1 more
TLDR
In this paper, an exact solution for the problem of a harmonic oscillator of frequency 0 and mass varying with time according to M = MO cos2?t is presented, which is closely related to that of an oscillator with constant mass MO and frequency (?O2 +?2)1/2.Abstract:
An exact solution is presented for the problem of a harmonic oscillator of frequency ?0 and mass varying with time according to M = MO cos2 ?t. The solution is closely related to that of an oscillator of constant mass MO and frequency (?O2 + ?2)1/2. Pseudostationary and quasicoherent states are discussed. Applications in quantum optics are foreseen.read more
Citations
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Journal ArticleDOI
Exact solvability of potentials with spatially dependent effective masses
TL;DR: In this paper, the exact solvability of the Schroedinger equation was discussed, and it was shown that operators with linear dependence on the momentum are non-ambiguous.
Journal ArticleDOI
The quantum damped harmonic oscillator
TL;DR: In this article, the authors show that the path integral method yields the exact quantum theory of the Caldirola-Kanai Hamiltonian without violation of Heisenberg's uncertainty principle.
Journal ArticleDOI
The evolution operator technique in solving the Schrodinger equation, and its application to disentangling exponential operators and solving the problem of a mass-varying harmonic oscillator
C M Cheng,P C W Fung +1 more
TL;DR: In this article, a method for finding the evolution operator for the Schrodinger equation for the Hamiltonian expressible as H(t)=a1(t)J4+a2(t),J0+a3(t)) J- where J+, J0 and J- are the SU(2) group generators is presented.
Journal ArticleDOI
Harmonic oscillator with variable mass
TL;DR: In this paper, a general treatment of the quantal harmonic oscillator with variable mass is given, and several examples additional to those obtained by Colegrave and Abdalla for which a closed form solution is possible are given.
Journal ArticleDOI
Invariants for the time-dependent harmonic oscillator. I
R K Colegrave,M. Sebawe Abdalla +1 more
TL;DR: In this paper, two equivalent linear invariants and two equivalent quadratic invariants are obtained for a harmonic oscillator with variable mass or with variable frequency for damped oscillators.
References
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Book
Quantum Statistical Properties of Radiation
TL;DR: In this paper, Dirac Formulation of Quantum Mechanics Elementary Quantum Systems Operator Algebra Quantization of the Electromagnetic Field Interaction of Radiation with Matter Quantum Theory of Damping--Density Operator Methods Quantum Theory-Langevin Approach Lamb's Semiclassical Theory of a Laser [1] Statistical properties of a laser Appendices Index
Journal ArticleDOI
On the quantum mechanical treatment of dissipative systems
TL;DR: In this article, two types of nonlinear Hamiltonians are investigated which describe quantum mechanically a particle moving subject to a linear viscous force under the influence of a conservative force: the conventional explicitly time-dependent one and an alternative class of non-linear Hamiltonian.
Journal ArticleDOI
Coherent states and the resonance of a quantum damped oscillator
V. V. Dodonov,Vladimir I. Man’ko +1 more
TL;DR: In this article, a quantum-mechanical model of a damped harmonic oscillator with time-independent and time-dependent parameters is studied in the framework of the linear Schr\"odinger equation with a Hermitian nonstationary Hamiltonian.
Journal ArticleDOI
Harmonic oscillator with exponentially decaying mass
R K Colegrave,M. Sebawe Abdalla +1 more
TL;DR: In this paper, the problem of a harmonic oscillator with varying mass parameter is reduced by canonical transformation to the corresponding constant mass problem and is solved in the case of an exponentially decaying mass.
Journal ArticleDOI
A Canonical Description of the Fabry-pérot Cavity
R K Colegrave,M. Sebawe Abdalla +1 more
TL;DR: In this article, the authors extended the quantal description of a cavity from the case of constant mass to that of variable mass, corresponding to a decaying or driven cavity, in such a way that both Maxwell's equations and quantal equations of motion are invariant.
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An Exact Quantum Theory of the Time‐Dependent Harmonic Oscillator and of a Charged Particle in a Time‐Dependent Electromagnetic Field
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Coherent states and the resonance of a quantum damped oscillator
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