Semi-classical analysis of Schrodinger operators and compactness in the   d-bar-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 Schr\"{o}dinger operators with magnetic fields and the relationship of this behavior with compactness in the $\bar\partial$-Neumann problem on Hartogs domains in $\C^2$ 
Siqi Fu and Emil J. Straube