Transmission through locally periodic potentials in space-fractional quantum mechanics

•Transmission probabilities are calculated for a chain of NN Dirac-delta barriers.•Transmission probabilities are calculated for a chain of NN square barriers.•Transfer-matrix approach is used for calculation of transmission probabilities.•Bandlike structures emerge even for a small number of barriers.•Bandlike structures are more apparent for smaller values of Lévy index considered.

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)T(N) for a particle in a chain of NN Dirac-δδ barriers and, for the other case, a chain of NN square barriers. We use a transfer-matrix (M-matrix) approach in the context of SFQM to obtain equations for T(N)T(N). For both systems, bandlike structures emerge even for a small number of barriers of as low as N=4N=4 and are more apparent for lower values of Lévy index αα considered.