Quantum effective force in an expanding infinite square-well potential and Bohmian perspective

TL;DR

This paper investigates the quantum effective force experienced by a particle in an expanding infinite square well, revealing nonlocal boundary effects and analyzing Bohmian trajectories to understand quantum boundary interactions.

Contribution

It introduces a quantum effective force related to the quantum potential gradient and explores its dynamics in an expanding well, providing a Bohmian perspective on boundary effects.

Findings

The effective force equals the expectation value of the quantum potential gradient.

Boundary expansion influences the particle even when far from walls.

Bohmian trajectories illustrate nonlocal boundary effects.

Abstract

The Schr\"{o}dinger equation is solved for the case of a particle confined to a small region of a box with infinite walls. If walls of the well are moved, then, due to an effective quantum nonlocal interaction with the boundary, even though the particle is nowhere near the walls, it will be affected. It is shown that this force apart from a minus sign is equal to the expectation value of the gradient of the quantum potential for vanishing at the walls boundary condition. Variation of this force with time is studied. A selection of Bohmian trajectories of the confined particle is also computed.