Transient effect of a free particle wave packet in the hydrodynamic formulation of the time-dependent Schrödinger equation

2003 ◽  
Vol 94 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Ravi K. Vadapalli ◽  
Charles A. Weatherford ◽  
Ioana Banicescu ◽  
Ricolindo L. Cariño ◽  
Jianping Zhu
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Schrodinger Equation ◽  
Free Particle ◽  
Time Dependent ◽  
Transient Effect

Solving Time-dependent Schrödinger Equation Using Gaussian Wave Packet Dynamics

2018 ◽  
Vol 73 (9) ◽  
pp. 1269-1278
Author(s):  
Min-Ho Lee ◽  
Chang Woo Byun ◽  
Nark Nyul Choi ◽  
Dae-Soung Kim
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Wave Packet Dynamics

QUANTUM DYNAMICS OF WAVE PACKET IN HARMONIC POTENTIAL

2005 ◽  
Vol 19 (24) ◽  
pp. 3745-3754
Author(s):  
ZHAN-NING HU ◽  
CHANG SUB KIM
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Quantum Dynamics ◽  
Schrodinger Equation ◽  
Analytic Solution ◽  
Nonlinear Differential Equations ◽  
Time Dependent ◽  
Dimensional System ◽  
Two Dimensional ◽  
Vibrational States

In this paper, the analytic solution of the time-dependent Schrödinger equation is obtained for the wave packet in two-dimensional oscillator potential. The quantum dynamics of the wave packet is investigated based on this analytic solution. To our knowledge, this is the first time we solve, analytically and exactly this kind of time-dependent Schrödinger equation in a two-dimensional system, in which the Gaussian parameters satisfy the coupled nonlinear differential equations. The coherent states and their rotations of the system are discussed in detail. We find also that this analytic solution includes four kinds of modes of the evolutions for the wave packets: rigid, rotational, vibrational states and a combination of the rotation and vibration without spreading.

scholarly journals On a Conjecture regarding Fisher Information

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Angelo Plastino ◽  
Guido Bellomo ◽  
Angel Ricardo Plastino
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Free Particle ◽  
Quantum Probability ◽  
Time Dependent ◽  
Theoretical Physics ◽  
One Dimension ◽  
Pure States ◽  
Time Dependent Solution

Fisher’s information measureIplays a very important role in diverse areas of theoretical physics. The associated measuresIxandIp, as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The productIxIphas been conjectured to exhibit a nontrivial lower bound in Hall (2000). More explicitly, this conjecture says that for any pure state of a particle in one dimensionIxIp≥4. We show here that such is not the case. This is illustrated, in particular, for pure states that are solutions to the free-particle Schrödinger equation. In fact, we construct a family of counterexamples to the conjecture, corresponding to time-dependent solutions of the free-particle Schrödinger equation. We also conjecture that any normalizable time-dependent solution of this equation verifiesIxIp→0fort→∞.

Algorithm for computing a wave packet evolution of the time-dependent Schrödinger equation

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
A.A. Gusev ◽  
O. Chuluunbaatar ◽  
S.I. Vinitsky ◽  
A.G. Abrashkevich
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Schrodinger Equation ◽  
Time Dependent

scholarly journals On integrals associated with the free particle wave packet

2020 ◽  
Vol 26 (2) ◽  
pp. 257-262
Author(s):  
Alexander E. Patkowski
Keyword(s):  
Wave Packet ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Schrodinger Equation ◽  
Free Particle ◽  
Time Dependent ◽  
Half Integer ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Made In

AbstractWe discuss some properties of integrals associated with the free particle wave packet, {\psi(x,t)}, which are solutions to the time-dependent Schrödinger equation for a free particle. Some noteworthy discussion is made in relation to integrals which have appeared in the literature. We also obtain formulas for half-integer arguments of the Riemann zeta function.

TIME-DEPENDENT EVOLUTION OF A WAVE PACKET IN QUANTUM SYSTEMS

2008 ◽  
Vol 22 (24) ◽  
pp. 4225-4241
Author(s):  
CHI-SHUNG TANG ◽  
PI-GANG LUAN
Keyword(s):  
Charged Particle ◽  
General Solution ◽  
Schrödinger Equation ◽  
Wave Packet ◽  
Particle Motion ◽  
Schrodinger Equation ◽  
Quantum Systems ◽  
Time Dependent ◽  
Ehrenfest Theorem ◽  
Charged Particle Motion

We consider wave packet propagation in mesoscopic quantum systems. A number of approaches are compared to look at the general solution of a time-dependent Schrödinger equation and the validity of the Ehrenfest theorem. Detailed calculations are presented to illustrate the results of a charged particle motion in the time-dependent systems, and show that the Ehrenfest theorem is not directly applicable in topologically nontrivial systems.

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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