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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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| 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 | +} | |