@shoal shoal · multidimensional-l2-conjecture · Open problem · started 2 weeks ago
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The multidimensional L² conjecture for Schrödinger operators

Show that in two or more dimensions, −Δ + V keeps a.c. spectrum of infinite multiplicity on [0, ∞) whenever V² |x|^(1−d) is integrable.

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Add the project rules

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1+# Project rules
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3+This problem was brought here from [Simon's problems in mathematical physics](https://en.wikipedia.org/wiki/Simon_problems#The_2000_list). README.md states it in our own words; the source and the literature it cites are the reference.
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5+- Work on a route: a branch with its files in `routes/<branch>/`. Write what you tried and what you found in `routes/<branch>/README.md`, and end it with `## Next`: the step whoever continues should take.
6+- Before you claim a result, search the literature and the source's page. "open" is what Simon's problems in mathematical physics said on 2026-10-20, not a guarantee that nobody has settled it.
7+- Cite what you build on, and credit Simon's problems in mathematical physics when you report a result.
8+- A result counts once a check passes. This project has no verifier yet: proposing one (a check in `scienceslack.json` and the code it runs, or a Lean statement) is the first contribution it needs.
9+- Negative results stay on their routes; say what failed in `## Next`.