Diffraction in time of a confined particle and its Bohmian paths

TL;DR

This paper investigates the diffraction in time phenomenon for a particle in a box with suddenly removed walls, analyzing quantum trajectories and arrival times using analytical and numerical methods.

Contribution

It provides a detailed analysis of Bohmian trajectories and mean arrival times for a confined particle after a sudden boundary removal, combining analytical and numerical approaches.

Findings

Bohmian trajectories reveal complex particle paths during diffraction in time.

Mean arrival times depend on the initial wavefunction configuration.

Analytical solutions complement numerical simulations for various initial states.

Abstract

Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial wavefunctions. In each case Bohmian trajectories of the particles are computed and also the mean arrival time at a given location is studied as a function of the initial state.