Radial Basis Functions for the Time‐Dependent Schrödinger Equation
- Conference date: 19–25 September 2011
- Location: Halkidiki, (Greece)
We consider a novel discretization method for the time‐dependent Schrödinger 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.
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