A Relativistic One-Particle Time of Arrival Operator for a Free Spin-1/2 Particle in (1 + 1) Dimensions
arXiv:1509.00307 · doi:10.1016/j.aop.2015.03.018
Abstract
As a follow-up to a recent study in the spin-0 case [J. Bunao and E. A. Galapon, Ann. Phys. 353, 83-106 (2015)], we construct a one-particle Time of Arrival (TOA) operator conjugate to a Hamiltonian describing a free relativistic spin-1/2 particle in one spatial dimension. Upon transformation in a representation where the Hamiltonian is diagonal, it turns out that the constructed operator consists of an operator term whose action is the same as in the spin-0 case, and another operator term which commutes with the Hamiltonian but breaks invariance under parity inversion. If we must impose this symmetry on our TOA operator, then we can throw away so that the TOA operator is just .
Preprint. Please refer to the Annals of Physics for published version