Collocation method for fractional quantum mechanics
arXiv:0912.2562 · doi:10.1063/1.3511330
Abstract
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 (LSF), which discretizes the Schrödinger 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 WKB analysis is performed.
13 pages, 5 figures, 3 tables