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Title: Analysis of Schrodinger operators with inverse square potentials I: regularity results in 3D
Authors: Hunsicker, Eugenie
Li, Hengguang
Nistor, Victor
Uski, Ville
Keywords: Regularity of eigenfunctions
Schrodinger operator
Eigenvalue approximations
Inverse square potential
Weighted Sobolev spaces
Rate of convergence of numerical methods
Solid state physics
Issue Date: 2012
Publisher: Société des Sciences Mathématiques de Roumanie
Citation: HUNSICKER, E. ... et al, 2012. Analysis of Schrodinger operators with inverse square potentials I: regularity results in 3D. Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, 55 (2), pp. 157 - 178.
Abstract: Let V be a potential on R3 that is smooth everywhere except at a discrete set S of points, where it has singularities of the form Z/ 2, with (x) = |x − p| for x close to p and Z continuous on R3 with Z(p) > −1/4 for p 2 S. Also assume that and Z are smooth outside S and Z is smooth in polar coordinates around each singular point. We either assume that V is periodic or that the set S is finite and V extends to a smooth function on the radial compactification of R3 that is bounded outside a compact set containing S. In the periodic case, we let be the periodicity lattice and define T := R3/ . We obtain regularity results in weighted Sobolev space for the eigenfunctions of the Schr¨odinger-type operator H = − + V acting on L2(T), as well as for the induced k–Hamiltonians Hk obtained by restricting the action of H to Bloch waves. Under some additional assumptions, we extend these regularity and solvability results to the non-periodic case. We sketch some applications to approximation of eigenfunctions and eigenvalues that will be studied in more detail in a second paper.
Description: This article was published in the journal, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie and is available here with the kind permission of the publisher.
Sponsor: V.N. was partially supported by the NSF Grants OCI-0749202 and DMS-1016556. H.L. was partially supported by the NSF Grant DMS-1115714. E.H. was supported in part by Leverhulme Trust Project Assistance Grant F/00 261/Z.
Version: Submitted for publication
URI: https://dspace.lboro.ac.uk/2134/17171
Publisher Link: http://ssmr.ro/bulletin/volumes/55-2/node5.html
ISSN: 1220-3874
Appears in Collections:Published Articles (Maths)

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