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

Abstract

The Schrödinger 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.

Nonlocality and local causality in the Schrödinger equation with time-dependent boundary conditions

“…Bohmian trajectories in systems analogous to the one investigated here have been previously computed [29].…”

On the evolution of quantum non-equilibrium in expanding systems

“…The uniformly expanding one-dimensional cavity has already been considered from the point of view of the pilot-wave theory (see [21] and [22] for example). In the two-dimensional case, the explicit expression for the velocity field is…”

Quantum effective force and Bohmian approach to time-dependent traps

“…by specifying the initial condition r(0) = r 0 . In this context one can easily show that the time-derivative of the expectation value of actual momentum of the particle, p = ∇S, is given by [2] d dt…”

“…A class of such systems is systems with moving boundaries. Problem of a particle in a one-dimensional infinite square-well potential with one wall in uniform motion has been noticed from different aspects [1,2]. The concept of quantum effective force, time-derivative of expectation value of the momentum operator, was introduced in [3] in the context of the quantum deflection of ultracold particles from mirrors.…”