On the adiabaticity of continum states: tunnelling through a time-dependent barrier

The problem of tunnelling through a time-dependent delta-function barrier, V(x, t) =λτ/tδ(x), has been solved analytically for t≧0. The Massey parameter α=γτk/h{combining short stroke overlay} controls the tunnel process: For α≫1, a continuum electron with momentum h{combining short stroke overlay}k will adjust its wavefunction to the variable barrier; for α≪1 the change of the barrier is too sudden to allow for adjustment. The characteristic time τ is used to clarify the concept of a tunnelling time.