Discrete spectrum in the gaps of a perturbed pseudorelativistic hamiltonian

The pseudorelativistic Hamiltonian G1/2 = ((-i∇-A)2 + I)1/2 + W, x ∈ ℝd, d ≥ 2, is considered under wide conditions on potentials A(x), W(x). It is assumed that a real point λ is regular for G1/2. Let G1/2(α) ≃ G1/2 - αV, where α > 0, V(x) ≥ 0, and V ∈ Ld(ℝd). Denote by N(λ,α) the number of eigenvalues of G1/2(t) that cross the point λ as t increases from 0 to α. A Weyl-type asymptotics is obtained for N(λ,α) as α → ∞. Bibliography: 5 titles. © 2000 Kluwer Academic/Plenum Publishers.