The problem of discretizing continuum states appears in a number of contexts in electronic structure: scattering problems, photo-ionization cross-sections, resonances, etc. The numerical challenge is to represent extended states using finite computational domains. I will present a recent effort to understand these problems mathematically (with M-S. Dupuy) and numerical methods to compute these properties efficiently (with I. Duchemin, L. Genovese, E. Letournel and S. Ruget), with example applications in condensed matter physics and chemistry.
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