APPLICATION OF THE QUANTUM CLOCK OF SALECKER AND WIGNER TO THE TUNNELING TIME PROBLEM

Peres used Salecker and Wigner's prescription for a quantum clock in a theoretical study of time-of-flight determination of the velocity of a free particle. In the present paper, the quantum clock is applied to a closely related problem, determination of the average time spent in side a one-dimensional potential barrier V(z)THETA(z)THETA(d-z) by ini tially free ''incident'' electrons of energy E. For an opaque rectangu lar barrier straightforward application of the approach leads to a ''c locked'' result that differs by orders of magnitude from the result po stulated by Buttiker for the average ''intrinsic'' dwell time tau(D)(0 , d; E). It is shown that this difference can be eliminated by appropr iate choice of initial state for the ensemble of identical clocks and by applying to their average behaviour when coupled to tunneling parti cles the calibration determined for the corresponding ensemble of free ly running clocks. The difference that persists for more transparent b arriers is attributed, following Peres, to perturbation of the clock a nd/or particle dynamics during the measurement process. It is most ser ious in the limit d-->0 where the ratio of clocked to intrinsic times peaks at a value of about 1.6. Because of the nonlinear relation betwe en ''actual'' time (i.e. the parameter t in the Schrodinger equation) and uncalibrated clock time it does not seem possible to decompose the mean dwell time for an opaque barrier as ''measured'' by the quantum clock approach considered here into individual components associated w ith transmitted and reflected particles. This is consistent with the p oint of view that the ''tunneling time'', which refers only to the tra nsmitted particles, is not a meaningful concept within conventional in terpretations of quantum mechanics.