EIGENVALUE BOUNDS FOR SCHRODINGER OPERATORS WITH COMPLEX POTENTIALS. III

摘要

We discuss the eigenvalues Ej of Schrodinger operators - Delta+ V in L-2(R-d) with complex potentials V is an element of L-p, p < infinity. We show that (A) ReEj -> infinity implies Im E-j -> 0, and (B) ReEj -> E is an element of [ 0,8) implies (ImE(j)) is an element of l(q) for some q depending on p. We prove quantitative versions of (A) and (B) in terms of the L-p-norm of V.