Collocation method for fractional quantum mechanics

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

References in corpus (8)

• Fractional Schrodinger equation
• Fractional Quantum Mechanics
• Fractional Laplacian in Bounded Domains
• A variational sinc collocation method for strong-coupling problems
• Solving the Helmholtz equation for membranes of arbitrary shape
• Variational collocation on finite intervals
• A new method for studying the vibration of non-homogeneous membranes
• A new representation for non--local operators and path integrals

Cited by in corpus (2)

• A high-order nodal discontinuous Galerkin method for nonlinear fractional Schrödinger type equations
• Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well