, Volume 103, Issue 2, pp 177-240

Differential equations in the spectral parameter

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Abstract

We determine all the potentialsV(x) for the Schrödinger equation (−∂ x 2 +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)