Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case |
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| Authors: | M. Klaus Barry Simon |
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| Affiliation: | Department of Physics, Princeton University, Princeton, New Jersey 08540 USA |
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| Abstract: | Consider ?Δ + λV with V short range at a value λ0 where some eigenvalue e(λ) → 0 as λ ↓ λ0. We analyze two questions: (i) What is the leading order of e(λ), i.e., for what α does e(λ) ～ c(λ ? λ0)α? (ii) Is e(λ) analytic at λ = λ0 and, if not, what is the natural expansion parameter? The results are highly dimension dependent. |
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