Trajectory description of the quantum–classical transition for wave packet interference

Journal Article · Mon Aug 15 04:00:00 EDT 2016 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2016.06.001· OSTI ID:22560342

Chou, Chia-Chun

The quantum–classical transition for wave packet interference is investigated using a hydrodynamic description. A nonlinear quantum–classical transition equation is obtained by introducing a degree of quantumness ranging from zero to one into the classical time-dependent Schrödinger equation. This equation provides a continuous description for the transition process of physical systems from purely quantum to purely classical regimes. In this study, the transition trajectory formalism is developed to provide a hydrodynamic description for the quantum–classical transition. The flow momentum of transition trajectories is defined by the gradient of the action function in the transition wave function and these trajectories follow the main features of the evolving probability density. Then, the transition trajectory formalism is employed to analyze the quantum–classical transition of wave packet interference. For the collision-like wave packet interference where the propagation velocity is faster than the spreading speed of the wave packet, the interference process remains collision-like for all the degree of quantumness. However, the interference features demonstrated by transition trajectories gradually disappear when the degree of quantumness approaches zero. For the diffraction-like wave packet interference, the interference process changes continuously from a diffraction-like to collision-like case when the degree of quantumness gradually decreases. This study provides an insightful trajectory interpretation for the quantum–classical transition of wave packet interference.

• OSTI ID: 22560342
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Journal Issue: Complete Vol. 371; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFRACTION
HAMILTON-JACOBI EQUATIONS
INTERFERENCE
NONLINEAR PROBLEMS
PROBABILITY
SCHROEDINGER EQUATION
TIME DEPENDENCE
VELOCITY
WAVE FUNCTIONS
WAVE PACKETS