A New Concept for the Momentum of a Quantum Mechanical Particle in a Box

M. H. Al-Hashimi; U. -J. Wiese

paper

A New Concept for the Momentum of a Quantum Mechanical Particle in a Box

arXiv:2012.09596

Abstract

For a particle in a box, the operator $- i \partial_{x}$ is not Hermitean. We provide an alternative construction of a momentum operator $p = p_{R} + i p_{I}$ , which has a Hermitean component $p_{R}$ that can be extended to a self-adjoint operator, as well as an anti-Hermitean component $i p_{I}$ . This leads to a description of momentum measurements performed on a particle that is strictly limited to the interior of a box.

5 pages, 1 figure