Eigenvalue bounds for Schrödinger operators with complex potentials. II

By Rupert L. Frank, Barry Simon. 2015

157 citations recorded by the source corpus.

Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrodinger operator −Δ+Vin L2(Rν) with complex potential has absolute value at most a constant times ∥V∥(γ+ν/2)/γγ+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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c994ca4003866a2ce830e7e1adafc73ec0e9f516