Radial Basis Functions for the Time-Dependent Schrodinger Equation

摘要

We consider a novel discretization method for the time-dependent Schrodinger equation (TDSE). A spatial discretization based on a Galerkin approach with Gaussian RBFs gives a spectrally accurate approximation for unbounded domains. We show eigenvalue stability which allows for the operator to be combined with time-stepping methods specially suited for the TDSE. We also indicate how an exponential time-integrator can be implemented efficiently and how to interpolate solutions between different basis sets.