On the skeleton method and an application to a quantum scissor

Horia D. Cornean (1) , Pierre Duclos (2, 3) , Benjamin Ricaud (2, 3)

1 MATH. DEPT., AALBORG UNIVERSITY - Institut for Matematiske Fag, Aalborg university
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

In the spectral analysis of few one dimensional quantum particles interacting through delta potentials it is well known that one can recast the problem into the spectral analysis of an integral operator (the skeleton) living on the submanifold which supports the delta interactions. We shall present several tools which allow direct insight into the spectral structure of this skeleton. We shall illustrate the method on a model of a two dimensional quantum particle interacting with two infinitely long straight wires which cross one another at a certain angle : the quantum scissor.

Mots clés: spectral analysis; quantum scissor; delta interaction

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Horia D. Cornean, Pierre Duclos, Benjamin Ricaud. On the skeleton method and an application to a quantum scissor. Proceeding of Symposia in Pure Mathematics, 2008, 77, pp.657-672. ⟨hal-00206274⟩