Arrival Time from Hamiltonian with Non-Hermitian Boundary Term

Abstract

In this study, we developed a new method for finding the quantum probability density of arrival at the detector. The evolution of the quantum state restricted to the region outside of the detector is described by a restricted Hamiltonian that contains a non-Hermitian boundary term. The non-Hermitian term is shown to be proportional to the flux of the probability current operator through the boundary, which implies that the arrival probability density is equal to the flux of the probability current.