Communications in Mathematical Physics

, Volume 103, Issue 2, pp 177–240 | Cite as

Differential equations in the spectral parameter

  • J. J. Duistermaat
  • F. A. Grünbaum
Article

Abstract

We determine all the potentialsV(x) for the Schrödinger equation (−∂x2+V(x))∅=k2∅ such that some family of eigenfunctions ∅ satisfies a differential equation in the spectral parameterk of the formB(k, ∂k)ø=Θ(x)ø. For each suchV(x) we determine the algebra of all possible operatorsB and the corresponding functions Θ(x)

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • J. J. Duistermaat
    • 1
  • F. A. Grünbaum
    • 2
  1. 1.Mathematisch Instituut der Rijksuniversiteit UtrechtThe Netherlands
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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