Study of Certain Aspects of Anharmonic, Time-Dependent and Damped Harmonic Oscillator Systems

1989 ◽  
Vol 37 (10) ◽  
pp. 761-818 ◽  
Author(s):  
S. K. Bose ◽  
U. B. Dubey ◽  
N. Varma
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Damped Harmonic Oscillator

scholarly journals Integrals of the motion and green functions for time-dependent mass harmonic oscillators

2018 ◽  
Vol 64 (1) ◽  
pp. 30
Author(s):  
Surarit Pepore
Keyword(s):  
Harmonic Oscillator ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Green Functions ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Damped Harmonic Oscillator ◽  
System Trajectory ◽  
Dependent Mass ◽  
Motion Method

The application of the integrals of the motion of a quantum system in deriving Green function or propagator is established. The Greenfunction is shown to be the eigenfunction of the integrals of the motion which described initial points of the system trajectory in the phasespace. The explicit expressions for the Green functions of the damped harmonic oscillator, the harmonic oscillator with strongly pulsatingmass, and the harmonic oscillator with mass growing with time are obtained in co-ordinate representations. The connection between theintegrals of the motion method and other method such as Feynman path integral and Schwinger method are also discussed.

scholarly journals Constructing the time independent Hamiltonian from a time dependent one

Open Physics ◽  
2007 ◽  
Vol 5 (3) ◽  
Author(s):  
Michał Dobrski
Keyword(s):  
Dynamical System ◽  
Harmonic Oscillator ◽  
Time Dependent ◽  
Damped Harmonic Oscillator ◽  
Hamiltonian Dynamical System ◽  
Equivalent Time ◽  
New Time

AbstractIn this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.

TIME-DEPENDENT BOGOLIUBOV TRANSFORMATIONS AND THE DAMPED HARMONIC OSCILLATOR

1993 ◽  
Vol 08 (21) ◽  
pp. 1999-2009
Author(s):  
P. SHANTA ◽  
S. CHATURVEDI ◽  
V. SRINIVASAN ◽  
F. MANCINI
Keyword(s):  
Harmonic Oscillator ◽  
Master Equation ◽  
Time Dependent ◽  
Damped Harmonic Oscillator ◽  
Bogoliubov Transformations ◽  
Non Equilibrium

We derive the master equation for a damped harmonic oscillator, for any α, using time-dependent Bogoliubov transformations of non-equilibrium thermofield dynamics. This investigation naturally leads us to a physically and mathematically meaningful parametrization of the Bogoliubov matrix.

The exact evolution of the time-dependent driven damped harmonic oscillator with time-dependent mass and frequency

2002 ◽  
Vol 80 (12) ◽  
pp. 1559-1569 ◽  
Author(s):  
M Liang ◽  
B Yuan ◽  
K Zhong
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Classical Trajectory ◽  
Wave Functions ◽  
Time Dependent ◽  
Quantization Scheme ◽  
Dynamical Phase ◽  
Damped Harmonic Oscillator ◽  
Total Phase ◽  
Dependent Mass

Under a new quantization scheme, the exact wave functions of the time-dependent driven damped harmonic oscillator with time-dependent mass and frequency are obtained. The wave functions are shape-unchanging wave packet with the center moving along the classical trajectory. The total phase of the wave function is explicitly expressed as the sum of the dynamical phase and the geometrical phase. PACS Nos.: 03.65-w, 05.40-a

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