2011/04/22 by Françoise Truc, Truc, Francoise
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · doi:10.48550/arxiv.1104.4459
openalex publication_date 2011/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a Schrödinger operator H with a non-vanishing radial magnetic field B=dA and Dirichlet boundary conditions on the unit disk. We assume growth conditions on B near the boundary which guarantee in particular the compactness of the resolvent of this operator. Under some assumptions on an additional radial potential V the operator H + V has a discrete negative spectrum and we obtain an upper bound on the number of negative eigenvalues. As a consequence we get an upperbound of the number of eigenvalues of H smaller than any positive value, which involves the minimum of B and the square of the L2 -norm of A(r)/r, where A(r) is the specific magnetic potential defined as the flux of the magnetic field through the disk of radius r centerde in the origin.