  We introduce an arrival time operator which is self-adjoint and, unlike
previously proposed arrival time operators, has a close link to simple
measurement models. Its spectrum leads to an arrival time distribution which is
a variant of the Kijowski distribution (a re-ordering of the current) in the
large momentum regime but is proportional to the kinetic energy density in the
small momentum regime, in agreement with measurement models. A brief derivation
of the latter distribution is given. We make some simple observations about the
physical reasons for self-adjointness, or its absence, in arrival time
operators and in the momentum operator on the half-line and we also compare our
operator with the dwell time operator.
