Collocation Method for Fractional Quantum Mechanics

P. AMORE; FRANCISCO M. FERNÁNDEZ; C. P. HOFFMAN; R. A. SÁENZ

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Año: 2010 vol. 51 p. 2101 - 2117

0022-2488

We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schr¨odinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel–Kramers–Brillouin analysis is performed