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Results are obtained on resolvent expansions around zero energy for Schrödinger operators H=-Δ+V(x) on L2(Rm), where V(x) is a sufficiently rapidly decaying real potential. The emphasis is on a unified approach, valid in all dimensions, which does not require one to distinguish between ∫V(x)dx=0 and ∫V(x)dx≠0 in dimensions m=1,2. It is based on a factorization technique and repeated decomposition of the Lippmann–Schwinger operator. Complete results are given in dimensions m=1 and m=2.

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Let H be a Schrödinger operator on a Hilbert space H, such that zero is a nondegenerate threshold eigenvalue of H with eigenfunction Ψ 0. Let W be a bounded selfadjoint operator satisfying Ψ 0 , W Ψ 0 > 0. Assume that the resolvent (H − z) −1 has an asymptotic expansion around z = 0 of the form typical for Schrödinger operators on odd-dimensional spaces. Let H(ε) = H + εW for ε > 0 and small. We show under some additional assumptions that the eigenvalue at zero becomes a resonance for H(ε), in the time-dependent sense introduced by A. Orth. No analytic continuation is needed. We show that the imaginary part of the resonance has a dependence on ε of the form ε 2+(ν/2) with the integer ν ≥ −1 and odd. This shows how the Fermi Golden Rule has to be modified in the case of perturbation of a threshold eigenvalue. We give a number of explicit examples, where we compute the "location" of the resonance to leading order in ε. We also give results, in the case where the eigenvalue is embedded in the continuum, sharpening the existing ones.