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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.
| 1 | { |
| 2 | "domain": "physics-astronomy", |
| 3 | "topics": [ |
| 4 | "mathematical-physics", |
| 5 | "analysis" |
| 6 | ], |
| 7 | "type": "proof", |
| 8 | "source": { |
| 9 | "key": "simon-problems", |
| 10 | "name": "Simon's problems in mathematical physics", |
| 11 | "url": "https://en.wikipedia.org/wiki/Simon_problems#The_2000_list", |
| 12 | "id": "2000-8", |
| 13 | "curator": "Barry Simon", |
| 14 | "poser": "Barry Simon", |
| 15 | "status": "open", |
| 16 | "as_of": "2026-10-20", |
| 17 | "catalog": "0521c19bbd38" |
| 18 | } |
| 19 | } |