Tunneling time and energy uncertainty of surface-state electrons

We show that the tunneling time {τ} of a localized electron tunneling through a barrier modulated by a microwave field satisfies the relation {Δ}E{τ}={}, where the uncertainty {Δ}E in the energy of the coupled electron-field system is determined by the response of the electron to the time-dependent fields. We express {Δ}E as the expectation value of an operator and point out how it can be measured experimentally.