A new type of solution of the Schr\"odinger equation on a self-similar   fractal potential
  Scattering a quantum particle by a self-similar fractal potential on a Cantor set is investigated. We present a new type of solution of the functional equation for the transfer matrix of this potential, which was derived earlier from the Schr\"odinger equation. 
N L Chuprikov and O V Spiridonova