scholarly journals Exact time evolution and master equations for the damped harmonic oscillator

1997 ◽  
Vol 55 (1) ◽  
pp. 153-164 ◽  
Author(s):  
Robert Karrlein ◽  
Hermann Grabert
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Master Equations ◽  
Damped Harmonic Oscillator ◽  
Exact Time

scholarly journals ON THE QUANTIZATION OF DAMPED SYSTEMS

1993 ◽  
Vol 08 (21) ◽  
pp. 2037-2043 ◽  
Author(s):  
CHIHONG CHOU
Keyword(s):  
Differential Equation ◽  
Harmonic Oscillator ◽  
Time Evolution ◽  
Order Differential Equation ◽  
Second Order ◽  
First Order ◽  
Damped Harmonic Oscillator ◽  
Simple Observation ◽  
Second Order Differential Equation ◽  
Damped Systems

Based on a simple observation that a classical second order differential equation may be decomposed into a set of two first order equations, we introduce a Hamiltonian framework to quantize the damped systems. In particular, we analyze the system of a linear damped harmonic oscillator and demonstrate that the time evolution of the Schrödinger equation is unambiguously determined.

Exact time evolution of a classical harmonic-oscillator chain

1985 ◽  
Vol 31 (5) ◽  
pp. 3231-3236 ◽  
Author(s):  
J. Florencio ◽  
M. Howard Lee
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Exact Time

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

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