Transmission through locally periodic potentials in space-fractional quantum mechanics

We study transmission through locally periodic potentials in the framework of space-fractional quantum mechanics (SFQM). In particular, we calculate the transmission probabilities T ( N ) for a particle in a chain of N Dirac- δ barriers and, for the other case, a chain of N square barriers. We use a transfer-matrix (M-matrix) approach in the context of SFQM to obtain equations for T ( N ) . For both systems, bandlike structures emerge even for a small number of barriers of as low as N = 4 and are more apparent for lower values of Lévy index α considered.