Space-fractional Schrödinger equations for single and double fractional-dimensional Dirac-δ well systems

Abstract

We solve the space-fractional Schrödinger equations (SFSEs) with single and double fractional-dimensional Dirac-δ wells using the momentum-space approach. We accomplish this by introducing the generalized attractive Dirac comb in the λ-dimensional fractional space (0 < λ ≤ 1) to the SFSE and formulating an N × N matrix eigenvalue equation. Then we apply this method to solve the SFSEs with N = 1, 2 Dirac-δ wells.