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 Integrals of the motion and Green function for dual damped oscillators and coupled harmonic oscillators

2018 ◽  
Vol 64 (2) ◽  
pp. 150
Author(s):  
Surait Pepore
Keyword(s):  
Green Function ◽  
Harmonic Oscillators ◽  
Green Functions ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Coupled Harmonic Oscillators ◽  
System Trajectory ◽  
The Green Function ◽  
Damped Oscillators ◽  
Motion Method

The application for the integrals of the motion of a quantum system in deriving Green function or propagator is presented. The Green function is shown to be the eigenfunction of the integrals of the motion which described initial points of the system trajectory in the phase space. The exact expressions for the Green functions of the dual damped oscillators and the coupled harmonic oscillators are evaluated in co-ordinate representations. The relation between the integrals of the motion method and other methods such as Feynman path integral and Schwinger method are also presented.

JOINT ENTROPY OF THE HARMONIC OSCILLATOR WITH TIME-DEPENDENT MASS AND/OR FREQUENCY

2009 ◽  
Vol 23 (11) ◽  
pp. 2449-2461 ◽  
Author(s):  
ETHEM AKTÜRK ◽  
ÖZGÜR ÖZCAN ◽  
RAMAZAN SEVER
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Integral Method ◽  
Time Dependent ◽  
Joint Entropy ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Path Integral Method ◽  
Dependent Mass

Time-dependent joint entropy is obtained for harmonic oscillator with the time-dependent mass and frequency case. It is calculated by using time-dependent wave function obtained via Feynman path integral method. Variation of time dependence is investigated for various cases.

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

FEYNMAN PATH INTEGRAL REPRESENTATIONS FOR THE CLASSICAL DAMPED HARMONIC OSCILLATOR WITH STOCHASTIC FREQUENCY

2002 ◽  
Vol 16 (21) ◽  
pp. 793-806 ◽  
Author(s):  
LUIZ C. L. BOTELHO
Keyword(s):  
Harmonic Oscillator ◽  
Path Integral ◽  
Integral Solution ◽  
Integral Representations ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Damped Harmonic Oscillator

We propose a Feynman path-integral solution for classical damped harmonic oscillator motions with stochastic frequency.

Path integral for new models of time-dependent harmonic oscillators

2020 ◽  
Vol 17 (02) ◽  
pp. 2050029
Author(s):  
Badri Berrabah ◽  
Baya Bentag
Keyword(s):  
Harmonic Oscillator ◽  
Path Integral ◽  
Direct Method ◽  
Path Integrals ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
New Models ◽  
Normalized Solutions ◽  
Dependent Mass

We have presented a particular direct method to solve time-dependent quantum problems within the framework of path integrals by using explicitly time-dependent transformations. We have applied it to the case of harmonic oscillator with time-dependent mass and frequency. Some examples have illustrated the method used. From their exact propagators, normalized solutions have been obtained.

On the Quantization Problem of a Driven Harmonic Oscillator with Time Dependent Mass and Frequency

2003 ◽  
Vol 17 (18) ◽  
pp. 983-990 ◽  
Author(s):  
Swapan Mandal
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Present Solution ◽  
Quadratic Hamiltonian ◽  
Dependent Mass ◽  
Quantization Problem

The quantization of a driven harmonic oscillator with time dependent mass and frequency (DHTDMF) is considered. We observe that the driven term has no influence on the quantization of the oscillator. It is found that the DHTDMF corresponds the general quadratic Hamiltonian. The present solution is critically compared with existing solutions of DHTDMF.

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