Geometry of nodal sets and domains for eigenfunctions of Schroedinger operators |
Posted on:2009-12-06 | Degree:M.Sc | Type:Thesis |
University:McGill University (Canada) | Candidate:Haldane, Evan | Full Text:PDF |
GTID:2440390002491066 | Subject:Mathematics |
Abstract/Summary: | |
Perturbations of the Laplacian are known as Schrodinger operators. We pose a question about perturbations of eigenfunctions from multiple eigenspaces and answer the question in the case of the two-sphere. This is used to extend a previously known result about nodal sets of spherical harmonics to eigenfunctions of Schrodinger operators on the two-sphere. We also review some of the classical and recent results about nodal sets and domains for eigenfunctions of the Laplacian. |
Keywords/Search Tags: | Eigenfunctions, Nodal sets, Operators |
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