Communications in Mathematical Physics

, Volume 153, Issue 1, pp 117–146 | Cite as

Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators

  • Artemio González-López
  • Niky Kamran
  • Peter J. Olver


We completely determine necessary and sufficient conditions for the normalizability of the wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable Schrödinger operator on the line. Methods from classical invariant theory are employed to provide a complete list of canonical forms for normalizable quasi-exactly solvable Hamiltonians and explicit normalizability conditions in general coordinate systems.


Neural Network Statistical Physic Coordinate System Wave Function Normalizability Condition 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Artemio González-López
    • 1
  • Niky Kamran
    • 2
  • Peter J. Olver
    • 3
  1. 1.Department de Física Teórica IIUniversidad ComplutenseMadridSpain
  2. 2.Department of MathematicsMcGill UniversityMontréalCanada
  3. 3.Department of MathematicsUniversity of MarylandCollege ParkUSA

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