Spectral asymptotics for two-dimensional Schrödinger operators with strong magnetic fields

Abstract

Abstract. In this paper we study the perturbed quadratic Hamiltonian in two-dimensional case,Here, b is the strong constant magnetic field, ω = 0 is a fixed constant, and the potential V vanishes at infinity. For f ∈ C ∞ 0 ((−∞, 0); R) and b large enough, we give a full asymptotic expansion in powers of b −1 of the trace of f (P (b, ω)). Moreover, we also obtain a Weyl formula with optimal remainder estimate of the counting function of eigenvalues of P (b, ω) as b → ∞.