Quantum-classical comparison: arrival times and statistics

TL;DR

This paper compares classical and quantum arrival times for a wave packet scattering off a barrier, highlighting their differences and similarities, especially in the large mass limit, and explores particle statistics effects.

Contribution

It introduces a comparison framework between classical and quantum arrival times using Rosen's classical wave equation and analyzes particle statistics effects.

Findings

Agreement between classical and quantum results improves with increasing mass.

Differences in particle statistics affect distribution outcomes.

Classical Rosen's wave equation can be extended to two-body systems.

Abstract

Classical and quantum scattering of a non-Gaussian wave packet by a rectangular barrier is studied in terms of arrival times to a given detector location. A classical wave equation, proposed by N. Rosen [{\it{Am. J. Phys.}} {\bf 32} (1964) 377], is used to study the corresponding classical dynamics. Mean arrival times are then computed and compared for different values of initial wave packet parameters and barrier width. The agreement is improved in the large mass limit as one expects. A short comment on the possibility of generalization of Rosen's proposal to a two-body system is given. Differences in distributions of particles obeying different statistics are studied by considering a system composed of two free particles.