scholarly journals Time evolution, cyclic solutions and geometric phases for the generalized time-dependent harmonic oscillator

2004 ◽  
Vol 37 (4) ◽  
pp. 1345-1371 ◽  
Author(s):  
Qiong-Gui Lin
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Time Dependent ◽  
Geometric Phases ◽  
Generalized Time

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.

Time evolution of a time-dependent inverted harmonic oscillator in arbitrary dimensions

2012 ◽  
Vol 45 (11) ◽  
pp. 115301
Author(s):  
Guang-Jie Guo ◽  
Zhong-Zhou Ren ◽  
Guo-Xing Ju ◽  
Xiao-Yong Guo
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Time Dependent ◽  
Arbitrary Dimensions

SQUEEZING AND SOME OTHER CHARACTERISTICS OF TIME-DEPENDENT HARMONIC OSCILLATOR WITH VARIABLE MASS

1994 ◽  
Vol 08 (14n15) ◽  
pp. 917-927 ◽  
Author(s):  
A. JOSHI ◽  
S. V. LAWANDE
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Time Evolution ◽  
Evolution Operator ◽  
Variable Mass ◽  
Time Dependent ◽  
Integral Approach ◽  
Feynman Path ◽  
Time Evolution Operator ◽  
General Time

In this paper we investigate the time evolution of a general time-dependent harmonic oscillator (TDHO) with variable mass using Feynman path integral approach. We explicitly evaluate the squeezing in the quadrature components of a general quantum TDHO with variable mass. This calculation is further elaborated for three particular cases of variable mass whose propagator can be written in a closed form. We also obtain an exact form of the time-evolution operator, the wave function, and the time-dependent coherent state for the TDHO. Our results clearly indicate that the time-dependent coherent state is equivalent to the squeezed coherent state.

NEW NONCLASSICAL SOLUTION ON GENERALIZED PAUL TRAP TYPE: NONCLASSICAL STUDY

2000 ◽  
Vol 15 (16) ◽  
pp. 1071-1078
Author(s):  
BISWANATH RATH
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Annihilation Operator ◽  
Paul Trap ◽  
Simple Expression ◽  
Creation Operator ◽  
Time Dependent ◽  
Dependent Frequency ◽  
Generalized Time

New nonclassical solutions for the harmonic oscillator with generalized time-dependent frequency have been found. Simple expression on energy level, creation operator a†(t) and annihilation operator a(t) have been obtained. Using new solutions we want to show how to study squeezing.

Squeezing caused by a change of mass in a harmonic oscillator

1989 ◽  
Vol 67 (2-3) ◽  
pp. 152-154 ◽  
Author(s):  
Fan Hong-Yi ◽  
H. R. Zaidi
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Mass Change ◽  
Transformation Time

It is shown that a mass change in a harmonic oscillator generates a squeezing transformation. Time-independent as well as time-dependent transformations are investigated. An expression for the interaction Hamiltonian responsible for squeezing and the equations of motion for the time evolution are derived.

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