Time of arrival operator in the momentum space

A. M. Schlichtinger, A. Jadczyk

Published 2022-02-21, updated 2022-02-22Version 2

It is shown that in presence of certain external fields a well defined self-adjoint time operator exists, satisfying the standard canonical commutation relations with the Hamiltonian. Examples include uniform electric and gravitational fields with nonrelativistic and relativistic Hamiltonians. The physical intepretation of these operators is proposed in terms of time of arrival in the momentum space.