Geodesic
One-Dimensional Schr\"odinger Operator on the Half-Line: the Differential Equation for Eigenfunctions with Respect to the Spectral Parameter and an Analog of the Freud Equation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 3, pp. 84-88

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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.
Keywords: one-dimensional Schrödinger equation, eigenfunctions of the Schrödinger equation, spectral function.
Mots-clés : Freud equation 
@article{FAA_2007_41_3_a5,
     author = {V. S. Buslaev and V. Yu. Strazdin},
     title = {One-Dimensional {Schr\"odinger} {Operator} on the {Half-Line:} the {Differential} {Equation} for {Eigenfunctions} with {Respect} to the {Spectral} {Parameter} and an {Analog} of the {Freud} {Equation}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {84--88},
     publisher = {mathdoc},
     volume = {41},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2007_41_3_a5/}
}
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V. S. Buslaev; V. Yu. Strazdin. One-Dimensional Schr\"odinger Operator on the Half-Line: the Differential Equation for Eigenfunctions with Respect to the Spectral Parameter and an Analog of the Freud Equation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 3, pp. 84-88. http://geodesic.mathdoc.fr/item/FAA_2007_41_3_a5/