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Schrödinger operators with purely discrete spectrum


We prove $-\Delta +V$ has purely discrete spectrum if $V\geq 0$ and, for all $M$, $|{\{x\mid V(x) < M\}}|<\infty$ and various extensions.

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TitleSchrödinger operators with purely discrete spectrum
SourceMethods Funct. Anal. Topology, Vol. 15 (2009), no. 1, 61-66
MathSciNet MR2502639
CopyrightThe Author(s) 2009 (CC BY-SA)

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Barry Simon
Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, USA 17/10/2008

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Barry Simon, Schrödinger operators with purely discrete spectrum, Methods Funct. Anal. Topology 15 (2009), no. 1, 61-66.


@article {MFAT495,
    AUTHOR = {Simon, Barry},
     TITLE = {Schrödinger operators with purely discrete spectrum},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {15},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {61-66},
      ISSN = {1029-3531},
       URL = {},

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