Alternative momentum concept for a quantum mechanical particle in a box

For a particle in box, the operator p̂=−i∂x is not self-adjoint. We provide an alternative construction of momentum p̂R+ip̂I, which has two self-adjoint components p̂R and p̂I. This leads to description measurements performed on that strictly limited interior box size L, yields quantized values πn/L with n∈Z.Received 22 December 2020Revised 14 July 2021Accepted 15 September 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.L042008Published by American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasNonrelativistic wave equationQuantum formalismQuantum measurementsGeneral Physics