Communications in Mathematical Physics

, Volume 103, Issue 2, pp 177–240

Differential equations in the spectral parameter

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

DOI: 10.1007/BF01206937

Cite this article as:
Duistermaat, J.J. & Grünbaum, F.A. Commun.Math. Phys. (1986) 103: 177. doi:10.1007/BF01206937


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)

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