  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
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
WKB analysis is performed.
