GEOMETRIC PHASE IN A MESOSCOPIC LC CIRCUIT WITH ALTERNATING SOURCE

2006 ◽  
Vol 20 (32) ◽  
pp. 5373-5381
Author(s):  
YING-HUA JI ◽  
JU-JU HU ◽  
QING LIU ◽  
DAN ZOU
Keyword(s):  
Schrödinger Equation ◽  
Parameter Space ◽  
Geometric Phase ◽  
Schrodinger Equation ◽  
Invariant Operator ◽  
Time Dependent ◽  
Phase Factor ◽  
Evolution Path ◽  
Lc Circuit

In this paper, we examine a mesoscopic LC circuit with alternating source and solve its time-dependent Schrödinger equation by selecting a proper Hermitian invariant operator. We study LR geometric phase in mesoscopic circuit system. Our results indicate that LR geometric phase is present at all times. In the evolution of the circuit system, it is a geometric phase factor accumulated by the wavefunction of external source's interaction with circuit system after nonadiabatic and noncyclic evolution. Its property lies in that it depends on the evolution path of the system wavefunction in the parameter space.

WAVE FUNCTIONS OF TIME-DEPENDENT TWO COUPLED OSCILLATORS BY LEWIS–RIESENFELD METHOD

2006 ◽  
Vol 20 (09) ◽  
pp. 1087-1096 ◽  
Author(s):  
HONG-YI FAN ◽  
ZHONG-HUA JIANG
Keyword(s):  
Schrödinger Equation ◽  
Operator Theory ◽  
Coupled Oscillators ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Invariant Operator ◽  
Wave Functions ◽  
Time Dependent ◽  
General Solutions ◽  
Eigenvectors And Eigenvalues

For the two time-dependent coupled oscillators model we derive its time-dependent invariant in the context of Lewis–Riesenfeld invariant operator theory. It is based on the general solutions to the Schrödinger equation which is obtained and turns out to be the superposition of the generalized atomic coherent states in the Schwinger bosonic realization. The energy eigenvectors and eigenvalues of the corresponding time-independent Hamiltonian are also obtained as a by-product.

Introduction

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
State Level ◽  
Boltzmann Distribution ◽  
Theoretical Description ◽  
Time Dependent ◽  
Nuclear Dynamics ◽  
Molecular Reaction ◽  
Oppenheimer Approximation

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized state-to-state level is discussed. The theoretical description of these reactions based on the time-dependent Schrödinger equation and the Born–Oppenheimer approximation is introduced and the resulting time-dependent Schrödinger equation describing the nuclear dynamics is discussed. The chapter concludes with a brief discussion of matter at thermal equilibrium, focusing at the Boltzmann distribution. Thus, the Boltzmann distribution for vibrational, rotational, and translational degrees of freedom is discussed and illustrated.

Numerical Solution of the Time-Dependent Schrödinger Equation and Application toH+-H

1979 ◽  
Vol 43 (7) ◽  
pp. 512-515 ◽  
Author(s):  
Vida Maruhn-Rezwani ◽  
Norbert Grün ◽  
Werner Scheid
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
Time Dependent

scholarly journals On form-preserving transformations for the time-dependent Schrödinger equation

1999 ◽  
Vol 40 (7) ◽  
pp. 3268-3274 ◽  
Author(s):  
Federico Finkel ◽  
Artemio González-López ◽  
Niky Kamran ◽  
Miguel A. Rodrı́guez
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Time Dependent
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