Bound states for multiple Dirac-δ wells in space-fractional quantum mechanics

Journal Article · Wed Jan 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4861933· OSTI ID:22251651

Tare, Jeffrey D., E-mail: [e-mail]; Esguerra, Jose Perico H., E-mail: [e-mail] ^[1]

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1. National Institute of Physics, University of the Philippines, Diliman, Quezon City 1101 (Philippines)

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 space-fractional 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.

• OSTI ID: 22251651
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUND STATE
EIGENVALUES
EQUATIONS
MATHEMATICAL SPACE
MATRICES
POTENTIALS
QUANTUM MECHANICS
WAVE FUNCTIONS