Derives a second-order sum rule for eigenvalues of abstract Hamiltonian families and applies it to Lieb-Thirring bounds, Bessel zeros, and trace inequalities.
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Necessary and sufficient conditions are proven for Schrödinger operators to possess zero-energy bound states with bounded k-th position moments at the essential spectrum threshold.
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Eigenstates with Infinite Position Moments
Necessary and sufficient conditions are proven for Schrödinger operators to possess zero-energy bound states with bounded k-th position moments at the essential spectrum threshold.