On Lewis' exact invariant for the linear harmonic oscillator with time-dependent frequency

1991 ◽  
Vol 154 (1-2) ◽  
pp. 24-28 ◽  
Author(s):  
Bhimsen K. Shivamoggi ◽  
Lawrence Muilenburg
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Dependent Frequency ◽  
Linear Harmonic Oscillator ◽  
Exact Invariant

Algebraic time-ordering techniques and harmonic oscillator with time-dependent frequency

1986 ◽  
Vol 34 (4) ◽  
pp. 2646-2653 ◽  
Author(s):  
G. Dattoli ◽  
S. Solimeno ◽  
A. Torre
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Dependent Frequency

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.

LEWIS–RIESENFELD PHASES AND BERRY PHASES FOR THE HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS

2003 ◽  
Vol 17 (10) ◽  
pp. 2045-2052 ◽  
Author(s):  
LING LI ◽  
BO-ZANG LI
Keyword(s):  
Harmonic Oscillator ◽  
Invariant Theory ◽  
Berry Phase ◽  
Time Dependent ◽  
Quantum Invariant ◽  
Fixed Boundary ◽  
Dependent Frequency ◽  
Oscillating Boundary ◽  
Berry Phases ◽  
Frequency Harmonic

We use Lewis and Riesenfeld's quantum invariant theory to calculate the Lewis–Riesenfeld phases for a time-dependent frequency harmonic oscillator that is confined between a fixed boundary and a moving one. We also discuss the Berry phase for the system with a sinusoidally oscillating boundary.

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