Time-of-arrival states

Although one can show formally that a time-of-arrival operator cannot exist , one can modify the low-momentum behavior of the operator slightly so that it is self-adjoint. We show that such a modification results in the diffic ulty that the eigenstates are drastically altered. In an eigenstate of the modified time-of-arrival operator, the particle, at the predicted time of a rrival, is found far away from the point of arrival with probability 1/2. [ S1050-2947(99)03403-4].