Time of arrival operator in the momentum space

TL;DR

This paper demonstrates the existence of a well-defined self-adjoint time of arrival operator in momentum space under certain external fields, with proposed physical interpretation in terms of arrival time.

Contribution

It introduces a new class of self-adjoint time operators in momentum space for systems under specific external fields, expanding the theoretical framework of quantum time observables.

Findings

Existence of self-adjoint time operators in external fields

Examples include electric and gravitational fields

Proposed interpretation as time of arrival in momentum space

Abstract

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.