Collocation method for fractional quantum mechanics

Journal Article · Wed Dec 15 00:00:00 EST 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3511330· OSTI ID:21501207

Amore, Paolo; Hofmann, Christoph P; Saenz, Ricardo A ^[1]; Fernandez, Francisco M ^[2]

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1. Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico)
2. INIFTA (Conicet, UNLP), Division Quimica Teorica, Diagonal 113 y 64 S/N, Sucursal 4, Casilla de correo 16, 1900 La Plata (Argentina)

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 Schroedinger 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.

• OSTI ID: 21501207
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 12; Other Information: DOI: 10.1063/1.3511330; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
BOUNDARY-VALUE PROBLEMS
COMPARATIVE EVALUATIONS
CONVERGENCE
FUNCTIONS
LAPLACE EQUATION
LAPLACIAN
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
QUANTUM MECHANICS
SCHROEDINGER EQUATION
WKB APPROXIMATION
APPROXIMATIONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
EVALUATION
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
MATHEMATICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS