Jason Kaye (CCM/CCQ)

Title: An integral equation-based solver for the time-dependent Schrodinger equation

Abstract: will introduce a new numerical method for the solution of the time-dependent Schrodinger equation based on its reformulation as a Volterra integral equation. Versions of the method are available for both periodic problems and free space problems with suitable potentials. A spatially uniform vector potential may be included, which makes the solver applicable to simulations of light-matter interaction.

The integral equation approach offers several benefits. Notably, it avoids the need for artificial boundary conditions in the free space problem. It also avoids the complexity associated with time-dependent potentials arising in methods based on direct application of the unitary propagator. However, it requires computing expensive spacetime history-dependent integral transforms at each time step. I will show how this may be done efficiently using a Fourier method, leading to an FFT-based solver which is spectrally accurate in space and admits inexpensive high-order implicit time stepping.