Arrival time from the general theory of quantum time distributions

Abstract

We further develop the general theory of quantum time distributions introduced in [D. Jurman and H. Nikolić, Phys. Lett. A 396, 127247 (2021)] and apply it to find the distribution of arrival times at the detector. Even though the Hamiltonian in the absence of detector is hermitian, the time evolution of the system before detection involves dealing with a non-hermitian operator obtained from the projection of the hermitian Hamiltonian onto the region in front of the detector. Such a formalism eventually gives rise to a simple and physically sensible analytical expression for the arrival time distribution, for arbitrary wave packet moving in one spatial dimension with negligible distortion.