Beyond the classical Weyl and Colin de Verdière's formulas for Schrödinger operators with polynomial magnetic and electric fields

DOI10.5802/aif.2229zbMath1127.35028arXivmath/0406071OpenAlexW1607502981WikidataQ33936915 ScholiaQ33936915MaRDI QIDQ877550

Mitya Boyarchenko, Sergei Levendorskii

Publication date: 24 April 2007

Published in: Proceedings of the National Academy of Sciences, Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406071

zbMATH Keywords

Schrödinger operatorsspectral asymptoticsnilpotent Lie algebrasorbit method

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) General theory of partial differential operators (47F05) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Nilpotent and solvable Lie groups (22E25) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items (6)

On absence of embedded eigenvalues for schrÖdinger operators with perturbed periodic potentials ⋮ Stable homotopy hypothesis in the Tamsamani model ⋮ Beyond the classical Weyl and Colin de Verdière's formulas for Schrödinger operators with polynomial magnetic and electric fields ⋮ The maximal abelian dimension of linear algebras formed by strictly upper triangular matrices ⋮ Magnetic pseudo-differential Weyl calculus on nilpotent Lie groups ⋮ Uncertainty principles for magnetic structures on certain coadjoint orbits

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