On absence of embedded eigenvalues for Schrodinger operators with perturbed periodic potentials Academic Article

abstract

• The problem of absence of eigenvalues imbedded into the continuous spectrum is considered for a Schrdinger operator with a periodic potential perturbed by a sufficiently fast decaying "impurity" potential. Results of this type have previously been known for the one-dimensional case only. Absence of embedded eigenvalues is shown in dimensions two and three if the corresponding Fermi surface is irreducible modulo natural symmetries. It is conjectured that all periodic potentials satisfy this condition. Separable periodic potentials satisfy it, and hence in dimensions two and three Schrdinger operator with a separable periodic potential perturbed by a sufficiently fast decaying "impurity" potential has no embedded eigenvalues.

authors

• Kuchment, Peter

published proceedings

• COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

author list (cited authors)

• Kuchment, P., & Vainberg, B.

citation count

• 28

complete list of authors

• Kuchment, P||Vainberg, B

publication date

• January 2000

publisher

• Taylor & Francis  Publisher

published in

• COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS  Journal

keywords

• Embedded Eigenvalues
• Periodic Potential
• Schrodinger Operator

Digital Object Identifier (DOI)

• 10.1080/03605300008821568

start page

• 1809

end page

• 1826

volume

• 25

issue

• 9-10

URL

• http%3A%2F%2Fdx.doi.org%2F10.1080%2F03605300008821568