Dynamics of the shifted time of arrival with time-reversal symmetry for the free particle case

Abstract

The solutions to the time-energy canonical commutation relation can be obtained using the time kernel equation. One specific boundary condition corresponds to the time of arrival solution. Other solutions produced by the general boundary condition are the shifted time of arrival solutions. We investigate the dynamics of a shifted time of arrival solution for the free particle case which satisfies time-reversal symmetry. It is shown that it does not exhibit unitary arrival at the origin, which is the expected arrival point of the time of arrival term.