Band asymptotics on line bundles over \(\delta ^ 2\) (Q1082692)

The authors study the spectrum of the Schrödinger operator \(\Delta_ a+q\), where \(\Delta_ a\) is the Bochner-Laplace operator for odd connection a on Hermitian line bundle over \(S^ 2\) (i.e. \(i^*Q=-Q\), where Q is the curvature of a and \(i: S^ 2\to S^ 2\) antipodal map). They show that the spectrum of the Schrödinger operator forms ''bands'' of fixed width about the eigenvalues of the Laplacian associated to the SO(3)-invariant connection and describe the asymptotic distribution of eigenvalues in the ''band''.