Journal ArticleDOI
The quantum mechanical linearly damped forced oscillator
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In this article, a solution to the quantum mechanical linearly damped harmonic oscillator subjected to a time dependent driving force is presented, which allows the calculation of interesting quantum quantities such as the Green's function and the transition amplitudes between harmonic oscillators states.Abstract:
The solution is obtained to the quantum mechanical linearly damped harmonic oscillator subjected to a time dependent driving force. This solution allows the calculation of interesting quantum quantities such as the Green’s function and the transition amplitudes between harmonic oscillator states. The specific results for a harmonic driving force are given.read more
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The quantum damped driven harmonic oscillator
TL;DR: Using the Caldirola-Kanai Hamiltonian with an external driving force for the damped driven harmonic oscillator as the quantum dissipative system, the authors have exactly evaluated the propagator, wave function, uncertainty relation and the transition amplitudes by the Feynman path integral method as discussed by the authors.
Journal ArticleDOI
Dissipative quantum dynamics: solution of the generalized von Neumann equation for the damped harmonic oscillator
M Hensel,Hans Jürgen Korsch +1 more
TL;DR: In this paper, a generalized von Neumann equation describing dissipative time evolution of quantum systems is applied to a damped and driven harmonic oscillator, and the nonlinear operator equation is solved and from this solution the behaviour of the mean value (x) is extracted, including both amplitude and phaseshift relative to the driving force.
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Dissipation-induced transition of a simple harmonic oscillator.
TL;DR: Different from the previous studies in the literature, it is found that the Brownian motion makes the transitions between states of different parity possible.
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Damped quantum mechanical oscillators with thermal fluctuations
TL;DR: In this paper, the solution for the relevant Heisenberg operators of a quadratic time-dependent quantum mechanical Hamiltonian is presented in convolution form suitable for the inclusion of thermal fluctuations.
References
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Journal ArticleDOI
Exact solution of a time‐dependent quantal harmonic oscillator with damping and a perturbative force
TL;DR: In this article, the problem of quantal harmonic oscillators with damping and a time-dependent frequency acted on by a timedependent perturbative force is exactly solved, and the wavefunctions are found in Schrodinger representation using the theory of explicitly timedependent invariants and also by an expansion of the Feynman propagator.
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Time-dependent harmonic oscillators
TL;DR: In this paper, a formalism for a time-dependent harmonic oscillator is presented and the quantum-mechanical solution is developed and the Green's function is derived, and particular examples of runaway and dissipative behavior are considered.
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Transition amplitudes for time-dependent harmonic oscillators
TL;DR: In this paper, the Green's function for a time dependent harmonic oscillator was used to calculate the corresponding transition amplitudes of damped and runaway oscillators, and the Green function was applied to a time-dependent harmonic oscillators.
Journal ArticleDOI
Time dependent linear quantum systems
TL;DR: The solution to the linear Heisenberg equations which result from the most general quadratic time dependent Hamiltonian was developed in this article, and the Green's function was obtained, and the transition amplitudes between harmonic states were calculated.