  Although one can show formally that a time-of-arrival operator cannot exist,
one can modify the low momentum behaviour of the operator slightly so that it
is self-adjoint. We show that such a modification results in the difficulty
that the eigenstates are drastically altered. In an eigenstate of the modified
time-of-arrival operator, the particle, at the predicted time-of-arrival, is
found far away from the point of arrival with probability 1/2.
