No abstract

We study the tunneling problem from the general Smith–Volterra–Cantor (SVC) potential of finite length L characterized by the scaling parameter ρ and stage G. We show that the SVC( ρ) potential of stage G is a special case of the super periodic potential (SPP) of order G. By using the SPP formalism developed by us earlier, we provide the closed form expression of the tunneling probability T G( k) with the help of the q-Pochhammer symbol. The profile of T G( k) with wave vector k is found to saturate with increasing stage G. Very sharp transmission resonances are found to occur in this system, which may find applications in the design of sharp transmission filters.