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

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.
Authors:
;  [1]
  1. National Institute of Physics, University of the Philippines, Diliman, Quezon City 1101 (Philippines)
Publication Date:
OSTI Identifier:
22251124
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; EIGENVALUES; EQUATIONS; MATHEMATICAL SPACE; MATRICES; POTENTIALS; QUANTUM MECHANICS; WAVE FUNCTIONS