Scattered wave packet formalism for open quantum systems: Comparison with the non-Markovian time-dependent Schrödinger equation

2012 ◽  
Vol 327 (5) ◽  
pp. 1355-1364 ◽  
Author(s):  
Chia-Chun Chou ◽  
Robert E. Wyatt
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Schrodinger Equation ◽  
Open Quantum Systems ◽  
Scattered Wave ◽  
Quantum Systems ◽  
Time Dependent ◽  
Open Quantum

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.

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 Quantum Entanglement of Free Particles

2021 ◽  
Author(s):  
Roumen Tsekov
Keyword(s):  
Schrödinger Equation ◽  
Quantum Entanglement ◽  
Schrodinger Equation ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Integral Of Motion ◽  
Friction Forces ◽  
Correlation Decay ◽  
Free Particles ◽  
Over Time

In this paper, the Schrödinger equation is solved for many free particles and their quantum entanglement is studied via correlation analysis. Converting the Schrödinger equation in the Madelung hydrodynamic-like form, the quantum mechanics is extended to open quantum systems by adding Ohmic friction forces. The dissipative evolution confirms the correlation decay over time, but a new integral of motion is discovered, being appropriate for storing everlasting quantum information.

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

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

Open Physics ◽  
2005 ◽  
Vol 3 (4) ◽  
Author(s):  
Axel Schulze-Halberg
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Transport Phenomena ◽  
Quantum Systems ◽  
Time Dependent ◽  
Effective Masses ◽  
Dependent Mass ◽  
Position Dependent Mass

AbstractWe study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.

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