scholarly journals On the Canonical Transformation of Time-Dependent Harmonic Oscillator

2010 ◽  
Vol 2010 ◽  
pp. 1-4
Author(s):  
Akpan N. Ikot ◽  
Louis E. Akpabio ◽  
Ita O. Akpan ◽  
Michael I. Umo ◽  
Oladunjoye A. Awoga ◽  
...  
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Canonical Transformation ◽  
Momentum Space ◽  
Hamiltonian Operator ◽  
Momentum Operator ◽  
Time Dependent ◽  
Variable Transformation ◽  
Time Coordinate ◽  
Space Coordinate

We performed a two-variable canonical transformation on the time momentum operator, and without loss of generality we carried out a three-variable transformation on the coordinate and momentum space operators to trivialize the Hamiltonian operator of the system. Fortunately, this operation separates the time-coordinate and space coordinate naturally, and the wave function of the time-dependent Harmonic Oscillator is evaluated via the generator.

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

Wave function in the invariant representation and squeezed-state function of the time-dependent harmonic oscillator

1994 ◽  
Vol 50 (2) ◽  
pp. 1035-1039 ◽  
Author(s):  
Kyu Hwang Yeon ◽  
Hyon Ju Kim ◽  
Chung In Um ◽  
Thomas F. George ◽  
Lakshmi N. Pandey
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Time Dependent ◽  
State Function ◽  
Squeezed State ◽  
Invariant Representation

Investigation of Bohr Hamiltonian in the presence of time-dependent Manning–Rosen, harmonic oscillator and double ring shaped potentials

2016 ◽  
Vol 25 (09) ◽  
pp. 1650073 ◽  
Author(s):  
Hadi Sobhani ◽  
Hassan Hassanabadi
Keyword(s):  
Mathematical Method ◽  
Wave Function ◽  
Harmonic Oscillator ◽  
Physical Meaning ◽  
Time Dependent ◽  
Invariant Method ◽  
Double Ring ◽  
System A ◽  
Dependent Form

This paper contains study of Bohr Hamiltonian considering time-dependent form of two important and famous nuclear potentials and harmonic oscillator. Dependence on time in interactions is considered in general form. In order to investigate this system, a powerful mathematical method has been employed, so-called Lewis–Riesenfeld dynamical invariant method. Appropriate dynamical invariant for considered system has been constructed. Then its eigen functions and the wave function are derived. At the end, we discussed about physical meaning of the results.

WAVE FUNCTION OF THE TIME-DEPENDENT INVERTED HARMONIC OSCILLATOR

2002 ◽  
Vol 16 (17) ◽  
pp. 637-643 ◽  
Author(s):  
I. A. PEDROSA ◽  
I. GUEDES
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Time Dependent ◽  
Weber Function ◽  
Invariant Method ◽  
Dependent Mass

Time-dependent mass and frequency inverted harmonic oscillator is discussed in light of the Lewis and Reisenfeld invariant method. The wave function is found in terms of the Weber function. As an example, we derive the wave function of the inverted Caldirola-Kanai oscillator.

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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