MEASUREMENT OF TIME OF ARRIVAL IN QUANTUM-MECHANICS

It is argued that the time of arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then Delta t(A) similar to 1/E-k, where E-k is the ini tial kinetic energy of the particle. With a better accuracy, particles reflect off the measuring device, and the resulting probability distr ibution becomes distorted. It is shown that: a time-of-arrival operato r cannot exist, and that approximate time-of-arrival operators do not correspond to the measurements considered here.