Speed-up and slow-down of a quantum particle

TL;DR

This paper investigates how quantum particles' wave packets are affected by scattering potentials, revealing the complex nature of delays and the limitations of classical intuition in quantum delay analysis.

Contribution

It provides a detailed analysis of the amplitude distribution of delays in quantum scattering, highlighting the impracticality of defining a single delay in non-classical regimes.

Findings

Delay distributions are oscillatory and complex.

Classical delay concepts do not extend straightforwardly to quantum regimes.

Analysis includes tunneling, virtual states, and low barriers.

Abstract

We study non-relativistic propagation of Gaussian wave packets in one-dimensional Eckart potential, a barrier, or a well. In the picture used, the transmitted wave packet results from interference between the copies of the freely propagating state with different spatial shifts (delays), x', induced by the scattering potential. The Uncertainty Principle precludes relating the particle's final position to the delay experienced in the potential, except in the classical limit. Beyond this limit, even defining an effective range of the delay is shown to be an impracticable task, owing to the oscillatory nature of the corresponding amplitude distribution. Our examples include the classically allowed case, semiclassical tunnelling, delays induced in the presence of a virtual state, and scattering by a low barrier. The properties of the amplitude distribution of the delays, and its pole representation are studied in detail.