scholarly journals THE EXACT SOLUTION AND BERRY'S PHASE FOR THE GENERALIZED TIME-DEPENDENT HARMONIC OSCILLATOR

1991 ◽  
Vol 40 (1) ◽  
pp. 25
Author(s):  
GAO XIAO-CHUN ◽  
XU JIN-BO ◽  
QIAN TIE-ZHENG
Keyword(s):  
Exact Solution ◽  
Harmonic Oscillator ◽  
Time Dependent ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Generalized Time

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.

Exact solution of the generalized time-dependent Jaynes-Cummings Hamiltonian

1993 ◽  
Vol 178 (3-4) ◽  
pp. 239-244 ◽  
Author(s):  
J.L. Gruver ◽  
J. Aliaga ◽  
Hilda A. Cardeira ◽  
A.N. Proto
Keyword(s):  
Exact Solution ◽  
Time Dependent ◽  
Generalized Time

THREE ELABORATIONS ON BERRY’S CONNECTION, CURVATURE AND PHASE

1988 ◽  
Vol 03 (02) ◽  
pp. 285-297 ◽  
Author(s):  
R. JACKIW
Keyword(s):  
Conservation Laws ◽  
Quantum System ◽  
Canonical Transformation ◽  
Time Dependent ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Gauge Transformations ◽  
Constants Of Motion ◽  
Symmetry Transformations ◽  
Higher Order Corrections

We discuss how symmetries and conservation laws are affected when Berry’s phase occurs in a quantum system: symmetry transformations of coordinates have to be supplemented by gauge transformations of Berry’s connection, and consequently constants of motion acquire terms beyond the familiar kinematical ones. We show how symmetries of a problem determine Berry’s connection, curvature and, once a specific path is chosen, the phase as well. Moreover, higher order corrections are also fixed. We demonstrate that in some instances Berry’s curvature and phase can be removed by a globally well-defined, time-dependent canonical transformation. Finally, we describe how field theoretic anomalies may be viewed as manifestations of Berry’s phase.

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