Strong electric field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential
Abstract
We consider the Schrödinger operator with electric potential V, which decays at infinity, and magnetic potential A. We study the asymptotic behaviour for large values of the electric field coupling constant of the eigenvalues situated under the essentialspectrum lower bound. We concentrate on the cases of rapidly decaying V (e.g. V ∈ L ^{ m/2}(&R;^{ m }) for m ≥ 3) and arbitrary A, or slowly decaying V (i.e. V( x ∼  x^{ α }, α ∈ (0,2), as  x → ∞) and magnetic potentials A corresponding to constant magnetic fields B = curl A.
 Publication:

Letters in Mathematical Physics
 Pub Date:
 January 1991
 DOI:
 10.1007/BF00414634
 Bibcode:
 1991LMaPh..21...41R
 Keywords:

 35P20;
 81C10