The Variational Structure of Riesz Means
We establish the variational structure of Riesz means of negative eigenvalues of Schrödinger operators. For Hₕ(y) = −h²Δ − y(x) on L²(ℝᵈ), with negative eigenvalues λₙ = −κₙ² and L²-normalised eigenfunctions ψₙ, the Hellmann–Feynman theorem and the chain rule yield, for every Riesz order γ > ½, the functional identityδ/δy(x) ∑ₙ κₙ^(2γ) = γ ∑ₙ κₙ^(2γ−
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