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A novel application of a Fourier integral representation of bound states in quantum mechanics Am.Using the momentum-space approach, we obtain bound states for multiple Dirac-δ wells in the framework of space-fractional quantum mechanics. Introducing first an attractive Dirac-comb potential, i.e., Dirac comb with strength − g (g > 0), in the spacefractional Schrödinger equation we show that the problem of obtaining eigenenergies of a system with N Dirac-δ wells can be reduced to a problem of obtaining the eigenvalues of an N × N matrix. As an illustration we use the present matrix formulation to derive expressions satisfied by the bound-state energies of N = 1, 2, 3 delta wells. We also obtain the corresponding wave functions and express them in terms of Fox's H-function. C 2014 AIP Publishing LLC. [http://dx.

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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.