The solutions of the generalized classical and quantum harmonic oscillators with time dependent mass, frequency, two-photon parameter and external force: The squeezing effects

2010 ◽  
Vol 283 (23) ◽  
pp. 4685-4695 ◽  
Author(s):  
Shailendra Kumar Singh ◽  
Swapan Mandal
Keyword(s):  
External Force ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Two Photon ◽  
Photon Parameter ◽  
Dependent Mass

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.

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.

Bisporphyrin connected by tetrathiafulvalene

2009 ◽  
Vol 13 (01) ◽  
pp. 114-121 ◽  
Author(s):  
Kazuya Ogawa ◽  
Yasunori Nagatsuka
Keyword(s):  
Cross Section ◽  
Density Functional ◽  
Polar Solvent ◽  
Soret Band ◽  
Oxidation Potential ◽  
Time Dependent ◽  
Photon Absorption ◽  
Functional Theory ◽  
Two Photon Absorption ◽  
Two Photon

A new porphyrintetrathiafulvalene composite, where two porphyrins are bridged by te trathiafulvalene (TTF) using acetylene bonds was synthesized. The Q-band of the monomeric porphyrin appears at 590 nm whereas that of the composite is red-shifted to 620 nm and intensified. The Soret band is also red-shifted from 427 nm to 435 nm and much broadened, indicating the expansion of π-conjugation over the porphyrin and tetrathiafulvalene units. The HOMOs and LUMOs were calculated using time-dependent density functional theory. Voltammetric experiments revealed that the first oxidation potential of the TTF moiety in the composite was shifted by +155 mV compa red with TTF in the absence of composite. The effective two-photon absorption (2PA) cross section values were measured by using a nanosecond open aperture Z-scan method. The maximum effective 2PA cross section values were obtained at 760 nm, as 7300 GM in benzonitrile and 5900 GM in toluene. The values obtained in the polar solvent were 1.2 to 1.5 times larger than those in the nonpolar solvent.

Time-dependent mass spectra and breakdown graphs. 17. Naphthalene and phenanthrene

1993 ◽  
Vol 97 (47) ◽  
pp. 12282-12290 ◽  
Author(s):  
Yehiel Gotkis ◽  
Maria Oleinikova ◽  
Mor Naor ◽  
Chava Lifshitz
Keyword(s):  
Mass Spectra ◽  
Time Dependent ◽  
Dependent Mass
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