Space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ potential: Central Dirac-δ well and barrier cases

Abstract

We solve the space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ (QTD-δ) potential for all energies using the momentum-space approach. For the E < 0 solution, we consider two cases, i.e., when the strengths of the potential are V0 > 0 (QTD-δ potential with central Dirac-δ well) and V0 < 0 (QTD-δ potential with central Dirac-δ barrier) and derive expressions satisfied by the bound-state energy. For all fractional orders α considered, we find that there is one eigenenergy when V0 > 0, and there are two eigenenergies when V0 < 0. We also obtain both bound- and scattering-state (E > 0) wave functions and express them in terms of Fox's H-function.