Eigenvalue Bounds for Schrödinger Operators with Complex Potentials. Ii Rupert L. Frank and Barry Simon
نویسنده
چکیده
Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrödinger operator −∆+ V in L(R) with complex potential has absolute value at most a constant times ‖V ‖ γ+ν/2 for 0 < γ ≤ ν/2 in dimension ν ≥ 2. We prove this conjecture for radial potentials if 0 < γ < ν/2 and we ‘almost disprove’ it for general potentials if 1/2 < γ < ν/2. In addition, we prove various bounds that hold, in particular, for positive eigenvalues.
منابع مشابه
Eigenvalue Bounds for Schrödinger Operators with Complex Potentials. Ii
Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrödinger operator −∆ + V in L(R) with complex potential has absolute value at most a constant times ‖V ‖ γ+ν/2 for 0 < γ ≤ ν/2 in dimension ν ≥ 2. We prove this conjecture for radial potentials if 0 < γ < ν/2 and we ‘almost disprove’ it for general potentials if 1/2 < γ < ν/2. In addition, we prove various bounds that hold...
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