Eigenvalues of a periodic Schrödinger operator perturbed by a fast decaying potential

Let [ λ,  μ] be an interval contained in a spectral gap of a periodic Schrödinger operator H. Consider H( α) = H − αV, where V is a fast decaying positive function. We study the asymptotic behavior of the number of eigenvalues of H( α) in [ λ,  μ] as α → ∞.