Squeezing in harmonic oscillator with time-dependent mass and frequency

1990 ◽  
Vol 105 (5) ◽  
pp. 497-506 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Dependent Mass

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.

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.

Coherent states and geometric phases of a generalized damped harmonic oscillator with time-dependent mass and frequency

2014 ◽  
Vol 28 (26) ◽  
pp. 1450177 ◽  
Author(s):  
I. A. Pedrosa ◽  
D. A. P. de Lima
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Quantum Invariant ◽  
Dynamical Phase ◽  
Special Cases ◽  
Berry Phases ◽  
Dependent Mass

In this paper, we study the generalized harmonic oscillator with arbitrary time-dependent mass and frequency subjected to a linear velocity-dependent frictional force from classical and quantum points of view. We obtain the solution of the classical equation of motion of this system for some particular cases and derive an equation of motion that describes three different systems. Furthermore, with the help of the quantum invariant method and using quadratic invariants we solve analytically and exactly the time-dependent Schrödinger equation for this system. Afterwards, we construct coherent states for the quantized system and employ them to investigate some of the system's quantum properties such as quantum fluctuations of the coordinate and the momentum as well as the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary system. Finally, we evaluate the dynamical and Berry phases for three special cases and surprisingly find identical expressions for the dynamical phase and the same formulae for the Berry's phase.

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

THE FRACTIONAL CALCULUS OF VARIATIONS FROM EXTENDED ERDÉLYI-KOBER OPERATOR

2009 ◽  
Vol 23 (16) ◽  
pp. 3349-3361 ◽  
Author(s):  
AHMAD RAMI EL-NABULSI
Keyword(s):  
Fractional Calculus ◽  
Harmonic Oscillator ◽  
Calculus Of Variations ◽  
Fractional Derivatives ◽  
Time Dependent ◽  
Dissipative Systems ◽  
Hamilton Equations ◽  
Different Types ◽  
Fractional Calculus Of Variations ◽  
Dependent Mass

Fractional calculus of variations (FCV) has recently attracted considerable attention as it is deeply related to the fractional quantization procedure. In this work, the FCV from extended Erdélyi-Kober fractional integral is constructed. Our main goal is to exhibit a general treatment for dissipative systems, in particular the harmonic oscillator (HO) that has time-dependent mass and time-dependent frequency. The general linear equation of damped Erdélyi-Kober harmonic oscillator is constructed from which a time-dependent mass generalized law was derived exhibiting different types of behavior. This relatively new time-dependent mass law permits us to point out several possible cases simultaneously in contrast to many models discussed in the literature and without making use of any types of fractional derivatives. Some results on Hamiltonian part, namely Hamilton equations for the damped HO were obtained and discussed in detail.

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