Larmor clock reexamined.

Abstract

The Larmor clock, a thought experiment designed by Baz' to measure scattering times, is reexamined in the context of one-dimensional tunneling by wave packets, narrow in wave-number space, through arbitrary static barriers. It is shown that the Larmor clock is, in general, inaccurate when used on a single Fourier component, i.e., on a stationary state. A reliable Larmor clock depends for its operation on properly designed wave packets. Precise conditions for its reliability are given. Thus, the apparent conflict between previous Larmor clock results for tunneling times, and results arrived at by other methods, is removed. When properly set, the Larmor clock shows the classic phase times. Stationary-state calculations of Larmor and dwell ``times'' are shown to represent coherent superpositions of, in general, widely different collision events. The relative merits of the Larmor clock and the center-of-gravity clock are discussed. Finally, it is shown that, for an arbitrary symmetric potential, the reflection and transmission times coincide.