Some Remarks on the Spectrum of the Magnetic Stark Hamiltonians

The main purpose of this note is to study spectral properties of the Stark magnetic Hamiltonian : , on the Hilbert space L 2 (R 2 ). We show that if the potential V satisfies some mild regularity conditions and is sufficiently decaying at infinity, then the operator H(μ, ϵ) has possibly at most a finite number of eigenvalues.