Point interactions in two diemsions: Basic properties, approximations and applications to solid state physics.

On etudie rigoureusement l'operateur de Schrodinger formellement donne par H=−Δ−μδ(•−y) dans L 2 (R 2 ) et on montre comment l'approcher en termes d'hamiltoniens a courte portee transformes d'echelles. On considere des questions semblables pour l'operateur H=−Δ−Σ j=1 N μ j δ(•−y j ), N∈N. On etudie les proprietes spectrales du modele a un electron d'un cristal a 2 dimensions avec des interactions ponctuelles

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