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 ΔEτ=h, where the uncertainty ΔE in the energy of the coupled electron-field system is determined by the response of the electron to the time-dependent fields. We express ΔE as the expectation value of an operator and point out how it can be measured experimentally