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Buslaev, V. S.; Strazdin, V. Yu.

One-dimensional Schrödinger operator on the half-line: the differential equation for eigenfunctions with respect to the spectral parameter and an analog of the Freud equation. (English) Zbl 1168.34367

Funct. Anal. Appl. 41, No. 3, 237-240 (2007); translation from Funkts. Anal. Prilozh. 41, No. 3, 84-88 (2007).
Summary: It is shown that the eigenfunctions of the Schrödinger operator on the half-line satisfy an explicitly constructed differential equation with respect to the spectral parameter. Such an equation was earlier obtained for orthogonal polynomials. An analog of the Freud equation is found.

Cited in 1 Document

MSC:

34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34L05 General spectral theory of ordinary differential operators

Keywords:

one-dimensional Schrödinger equation; Freud equation; eigenfunctions of the Schrödinger equation; spectral function
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\textit{V. S. Buslaev} and \textit{V. Yu. Strazdin}, Funct. Anal. Appl. 41, No. 3, 237--240 (2007; Zbl 1168.34367); translation from Funkts. Anal. Prilozh. 41, No. 3, 84--88 (2007)
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References:

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