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Some generic properties of Schrödinger operators with radial potentials
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 6 / December 2019
- Published online by Cambridge University Press:
- 15 January 2019, pp. 1435-1451
- Print publication:
- December 2019
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- Article
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We consider a class of Schrödinger operators on
${\open R}^N$ with radial potentials. Viewing them as self-adjoint operators on the space of radially symmetric functions in 
$L^2({\open R}^N)$, we show that the following properties are generic with respect to the potential:
(P1) the eigenvalues below the essential spectrum are nonresonant (i.e., rationally independent) and so are the square roots of the moduli of these eigenvalues;
(P2) the eigenfunctions corresponding to the eigenvalues below the essential spectrum are algebraically independent on any nonempty open set.
