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

摘要

Published 2 January 2015 We solve the space-fractional Schr?dinger 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 Vo > 0 (QTD-δ potential with central Dirac-δ well) and Vo < 0 (QTD-δ potential with central Dirac-δ barrier) and derive expressions satisfied by the bound-state energy. For all fractional orders a considered, we find that there is one eigenenergy when Vo > 0, and there are two eigenenergies when Vo < 0. We also obtain both bound- and scattering-state (E > 0) wave functions and express them in terms of Fox's H-function.