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.


34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34L05 General spectral theory of ordinary differential operators
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[1] A. S. Fokas, A. R. Its, and A. V. Kitaev, Comm. Math. Phys., 147:2 (1992), 395–430. · Zbl 0760.35051
[2] Yang Chen, E. H. Mourad, and Ismail, J. Phys. A: Math. Gen., 30 (1997), 7817–7829. · Zbl 0927.33011
[3] L. D. Faddeev, Uspekhi Mat. Nauk, 14:4 (1959), 57–119.
[4] G. Moore, Comm. Math. Phys., 133:2 (1990), 261–304. · Zbl 0727.35134
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