Semi-classical analysis of Schrödinger operators and compactness in the ∂-Neumann problem ✩

We study the asymptotic behavior, in a “semi-classical limit,” of the first eigenvalues (i.e., the groundstate energies) of a class of Schrödinger operators with magnetic fields and the relationship of this behavior with compactness in the ∂-Neumann problem on Hartogs domains in C2.  2002 Elsevier Science (USA). All rights reserved