Spectral Pollution and How to Avoid It (With Applications to Dirac and Periodic Schr

@inproceedings{Lewin2008SpectralPA,
  title={Spectral Pollution and How to Avoid It (With Applications to Dirac and Periodic Schr},
  author={Mathieu Lewin and {\'E}ric S{\'e}r{\'e}},
  year={2008}
}
  • Mathieu Lewin, Éric Séré
  • Published 2008
  • Physics, Mathematics
  • This paper, devoted to the study of spectral pollution, contains both abstract results and applications to some self-adjoint operators with a gap in their essential spectrum occuring in Quantum Mechanics. First we consider Galerkin basis which respect the decomposition of the ambient Hilbert space into a direct sum $H=PH\oplus(1-P)H$, given by a fixed orthogonal projector $P$, and we localize the polluted spectrum exactly. This is followed by applications to periodic Schr\"odinger operators… CONTINUE READING

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