Semi-linear wave models with power non-linearity and scale-invariant time-dependent mass and dissipation, II

2018 ◽  
Vol 291 (11-12) ◽  
pp. 1859-1892 ◽  
Author(s):  
Alessandro Palmieri ◽  
Michael Reissig
Keyword(s):  
Time Dependent ◽  
Linear Wave ◽  
Scale Invariant ◽  
Wave Models ◽  
Dependent Mass

Semi-linear wave models with power non-linearity and scale-invariant time-dependent mass and dissipation

2016 ◽  
Vol 290 (11-12) ◽  
pp. 1779-1805 ◽  
Author(s):  
Wanderley Nunes do Nascimento ◽  
Alessandro Palmieri ◽  
Michael Reissig
Keyword(s):  
Time Dependent ◽  
Linear Wave ◽  
Scale Invariant ◽  
Wave Models ◽  
Dependent Mass

Theory of damped wave models with integrable and decaying in time speed of propagation

2016 ◽  
Vol 13 (02) ◽  
pp. 417-439 ◽  
Author(s):  
Marcelo Rempel Ebert ◽  
Michael Reissig
Keyword(s):  
Cauchy Problem ◽  
Wave Equations ◽  
Propagation Speed ◽  
Time Dependent ◽  
Scale Invariant ◽  
The Cauchy Problem ◽  
Wave Models ◽  
Speed Of Propagation ◽  
Loss Of Regularity

We study the Cauchy problem for damped wave equations with a time-dependent propagation speed and dissipation. The model of interest is [Formula: see text] We assume [Formula: see text]. Then we propose a classification of dissipation terms in non-effective and effective. In each case we derive estimates for kinetic and elastic type energies by developing a suitable WKB analysis. Moreover, we show optimality of results by the aid of scale-invariant models. Finally, we explain by an example that in some estimates a loss of regularity appears.

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.

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

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.

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