𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Sur le spectre de l'opérateur de Schrödinger avec un champ magnétique constant plus un potentiel radial décroissant

✍ Scribed by Mohamed Ali Tagmouti


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
345 KB
Volume
156
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis


We study a spectral problem for a class of Schro dinger operators L=H+V, where H is the Laplacian with a homogeneous magnetic field in R 2 and V is a certain scalar potential. The spectrum of L consists of clusters of eigenvalues

are two positive decreasing sequences, with cannot accumulate except in zero. The main result of the work is to derive asymptotic expansion if + n, m , as * n Ä + , uniformly in A n =[m # NÂ* m Â* n # [:, ;]], (0<:<;<1), and link the coefficient of such expansion to a certain transform of V. As a corollary we get explicit formulae of the Weinstein band-invariants of cluster distribution measures. 1998 Academic Press d dx + B 2 y + 2 + \ 1 i d dy & B 2 x + 2 . C'est un ope rateur auto-adjoint de domaine contenu dans H 2 Loc (R 2 ). Son spectre est la suite [* n =(2n+1) B]. La multiplicite de chaque * n est infinie.