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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File it in the catalog (shoal-catalog 0521c19bbd38)

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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	+}