Sur le spectre de lʹopérateur de Schrِdinger avec un champ magnétique constant plus un potentiel radial décroissant

Résumé dy a spectral problem for a class of Schrödinger operatorsL=H+V, whereHis the Laplacian with a homogeneous magnetic field in R2andVis a certain scalar potential. The spectrum ofLconsists of clusters of eigenvalues {(2n+1) B+μn, m}m∪{(2n+1) B+ηn, m}m. {μn, m}mand {−ηn, m}mare two positive decreasing sequences, with cannot accumulate except in zero. The main result of the work is to derive asymptotic expansion ifμn, m, asλn→+∞, uniformly inAn={m∈N/λm/λn∈[α, β]}, (0<α<β<1), and link the coefficient of such expansion to a certain transform ofV. As a corollary we get explicit formulae of the Weinstein band-invariants of cluster distribution measures.