Creating Coherent States in a Mesoscopic Josephson Junction

1998 ◽  
Vol 12 (25n26) ◽  
pp. 1069-1074
Author(s):  
Shao Bin ◽  
Jian Zou ◽  
Qianshu Li
Keyword(s):  
Schrödinger Equation ◽  
Coherent State ◽  
Josephson Junction ◽  
Ground State ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Hamiltonian Operator ◽  
Classical Field ◽  
The State ◽  
Time Dependent

We examine a system of mesoscopic Josephson junction driven by classical field and solve the time-dependent Schrödinger equation of the system with the help of the time-dependent invariant of the Hamiltonian operator. We show that the state of the system can evolve a pure coherent state when the junction is prepared initially in its ground state.

JAYNES-CUMMINGS MODEL AS A CASE STUDY FOR THE DERIVATION OF TIME-DEPENDENT SCHRÖDINGER EQUATION

2008 ◽  
Vol 22 (25n26) ◽  
pp. 4557-4564
Author(s):  
SUPITCH KHEMMANI ◽  
VIRULH SA-YAKANIT
Keyword(s):  
Schrödinger Equation ◽  
Coherent State ◽  
Linear Combination ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
State Representation ◽  
Field System ◽  
Single State ◽  
Special Case

The derivation of a time-dependent Schrödinger equation (TDSE) from a time-independent Schrödinger equation (TISE) in the coherent state representation is considered for the special case of a simple coupled atom-field system described by the soluble Jaynes-Cummings model. The derivation shows why, from the outset, a linear combination of energy eigenstates, instead of a single state, must be used in order to obtain a TDSE for general states. Moreover, this study leads to a method of solving a TDSE by simply solving a TISE.

The X (X = F, Cl, I) effect on the photoassociation of H+X→HX

2015 ◽  
Vol 14 (08) ◽  
pp. 1550062
Author(s):  
Wei Gao ◽  
Bin-Bin Wang ◽  
Yong-Chang Han ◽  
Shu-Lin Cong
Keyword(s):  
Schrödinger Equation ◽  
Vibrational Level ◽  
Ground State ◽  
Schrodinger Equation ◽  
Vibrational State ◽  
Time Dependent ◽  
Overlap Integral ◽  
Target State ◽  
Multiphoton Transition ◽  
Franck Condon

This work explores the vibrational state-selective photoassociation (PA) in the ground state of the HX (X = F, Cl, I) molecule by solving the time-dependent Schrödinger equation. For the three systems, the vibrational level of [Formula: see text] is set to be the target state and the PA probability of the target state is calculated and compared by considering different initial collision momentums. It is found that the PA probabilities are in accordance with Franck–Condon overlap integral for the HI and HCl systems, but it is not the case for the HF system. Moreover, for the HF system, it is shown that the PA probability of the target state is largest and the multiphoton transition is more likely to occur.

Coherent state theory of large amplitude collective motion

1976 ◽  
Vol 54 (19) ◽  
pp. 1941-1968 ◽  
Author(s):  
D. J. Rowe ◽  
R. Bassermann
Keyword(s):  
Schrödinger Equation ◽  
Large Amplitude ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Collective Motion ◽  
State Theory ◽  
Time Dependent ◽  
Hartree Fock ◽  
Starting Point ◽  
Reduced Representations

A theory of large amplitude collective motion of a many-particle system is presented, which is relevant, for example, to nuclear fission. The theory is a combination of techniques used in many areas of physics and mathematics. The starting point is the application of the time-dependent Schrödinger equation to generate invariant subspaces of the Hamiltonian in the Hartree–Fock approximation. This is a generalization of the group-theoretical device of generating orbits of a group in the construction of reduced representations. It is shown how solutions of the time-dependent Schrödinger equation can be expressed as instantaneous stationary states of a constrained static Hamiltonian. Thus contact is made with the traditional cranking models and constrained Hartree–Fock theories of large amplitude collective motion. The collective motion is quantized using the Hill–Wheeler–Griffin method of generator coordinates in a basis of generalized coherent states. One is thereby able to exploit much of the theory of harmonic oscillator coherent states, which have been so successfully used in the quantum theory of the laser. The resulting Schrödinger equation for the collective dynamics is expressed both in the Bargmann representation and in the more familiar Schrödinger representation. It is shown that solution of the Schrödinger equation in the small amplitude harmonic approximation reproduces the well-known RPA result. A pilot calculation for 28Si shows that application in large amplitude is also feasible.

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.

A NONADIABATIC QUANTUM MECHANICAL MONTE CARLO METHOD

2002 ◽  
Vol 13 (07) ◽  
pp. 909-915
Author(s):  
A. M. MAZZONE
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Efficient Solution ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Classical Dynamics ◽  
Hartree Fock

The problem addressed by this study is an efficient solution of the multi-particle time-dependent Schrödinger equation to be used under nonadiabatic conditions. To this purpose a solution combining classical dynamics for the nuclei and a quantum mechanical Monte Carlo method for the electrons is suggested as a practically feasible approach. As a show-case example, the method is applied to the evaluation of the ground state of H, He, H2 and H3 whose energy and structure is also obtained from stationary Hartree–Fock calculations.

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.

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