Topological properties of eigenoscillations in mathematical physics

DOI10.1134/S0081543811040031zbMath1229.35220OpenAlexW2011089961MaRDI QIDQ641936

Vladimir I. Arnold

Publication date: 25 October 2011

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543811040031

zbMATH Keywords

eigenfunctionsquantum mechanicssingularity theoryeigenoscillationsCourant's theorem

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Growth rate, Gelfand-Kirillov dimension (16P90) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) PDEs in connection with quantum mechanics (35Q40) Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) (58H10)

Related Items (6)

On Courant's nodal domain property for linear combinations of eigenfunctions. I ⋮ Sturm's theorem on zeros of linear combinations of eigenfunctions ⋮ A metric Sturm-Liouville theory in two dimensions ⋮ On the geometry of the set of symmetric matrices with repeated eigenvalues ⋮ Level sets of certain Neumann eigenfunctions under deformation of Lipschitz domains application to the extended Courant property ⋮ On Courant’s Nodal Domain Property for Linear Combinations of Eigenfunctions Part II

Cites Work

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• On the topology of the eigenfields
• Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect
• Structure of representations generated by vectors of highest weight

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