Complement to our article: "Considerations about the incompleteness of the Ehrenfest's theorem in quantum mechanics"

TL;DR

This paper provides an analytical solution to the eigenvalue problem for a punctiform charge in a 1D box with an electric field, discussing external forces and boundary effects in quantum mechanics.

Contribution

It offers a detailed analytical solution and discussion of forces for a punctiform charge in a confined quantum system under an electric field, complementing previous work.

Findings

Analytical eigenvalues for the system are derived.

Expressions for external forces on the charge are obtained.

Boundary effects in the presence of an electric field are analyzed.

Abstract

We describe the analytical solution of the eigenvalue problem introduced in our article mentioned in the title and relative to a punctiform electric charge confined in an one-dimensional box in the presence of an electric field. We also derive and discuss the analytical expressions of the external forces acting on the punctiform charge and associated with the boundaries of the one-dimensional box in the presence of the electric field.