On a certain semiclassical problem on Wiener spaces

We study asymptotic behavior of the spectrum of a Schrodinger type operator L-V(lambda) = L - lambda(2)V on the Wiener space as lambda --> infinity. Here L denotes the Ornstein-Uhlenbeck operator and V is a nonnegative potential function which has finitely many zero points. For some classes of potential functions, we determine the divergence order of the lowest eigenvalue. Also tunneling effect is studied.