Exact evolving states for a class of generalized time-dependent quantum harmonic oscillators with a moving boundary

2001 ◽  
Vol 291 (4-5) ◽  
pp. 190-196 ◽  
Author(s):  
Ling Li ◽  
Bo-Zang Li
Keyword(s):  
Moving Boundary ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Generalized Time

scholarly journals SCALING INVARIANCE IN A TIME-DEPENDENT ELLIPTICAL BILLIARD

2012 ◽  
Vol 22 (09) ◽  
pp. 1250207 ◽  
Author(s):  
DIEGO F. M. OLIVEIRA ◽  
MARKO ROBNIK
Keyword(s):  
Integrable System ◽  
Average Velocity ◽  
Moving Boundary ◽  
Time Dependent ◽  
Scaling Invariance ◽  
Energy Growth ◽  
Dynamical Properties ◽  
Scaling Arguments

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although the static elliptical billiard is an integrable system, after introducing time-dependent perturbation on the boundary the unlimited energy growth is observed. The behavior of the average velocity is described using scaling arguments.

GEOMETRIC PHASES, SQUEEZED QUANTUM STATES AND GAUSSIAN WAVE PACKET STATES OF RELIC GRAVITONS

2012 ◽  
Vol 18 ◽  
pp. 13-17
Author(s):  
K. BAKKE ◽  
I. A. PEDROSA ◽  
C. FURTADO
Keyword(s):  
Wave Packet ◽  
Linear Time ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Geometric Phases ◽  
Uncertainty Product ◽  
Quantized Field ◽  
Generalized Time

In this contribution, we discuss quantum effects on relic gravitons described by the Friedmann-Robertson-Walker (FRW) spacetime background by reducing the problem to that of a generalized time-dependent harmonic oscillator, and find the corresponding Schrödinger states with the help of the dynamical invariant method. Then, by considering a quadratic time-dependent invariant operator, we show that we can obtain the geometric phases and squeezed quantum states for this system. Furthermore, we also show that we can construct Gaussian wave packet states by considering a linear time-dependent invariant operator. In both cases, we also discuss the uncertainty product for each mode of the quantized field.

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.

Time-dependent coupled harmonic oscillators: Classical and quantum solutions

2014 ◽  
Vol 23 (09) ◽  
pp. 1450048 ◽  
Author(s):  
D. X. Macedo ◽  
I. Guedes
Keyword(s):  
Canonical Transformation ◽  
Unitary Transformation ◽  
Coupling Parameter ◽  
Wave Functions ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Classical Solutions ◽  
Arbitrary System ◽  
Coupled Harmonic Oscillators ◽  
The Masses

In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m1 = m2 = m0eγt, ω1 = ω01e-γt/2, ω2 = ω02e-γt/2 and k = k0.

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