Proceedings of the Japan Academy, Series A, Mathematical Sciences

Schrödinger operators with $n$ positive eigenvalues: an explicit construction involving complex-valued potentials

Serge Richard, Jun Uchiyama, and Tomio Umeda

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Abstract

An explicit construction is provided for embedding $n$ positive eigenvalues in the spectrum of a Schrödinger operator on the half-line with a Dirichlet boundary condition at the origin. The resulting potential is of von Neumann-Wigner type, but can be real-valued as well as complex-valued.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 92, Number 1 (2016), 7-12.

Dates
First available in Project Euclid: 28 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.pja/1451330560

Digital Object Identifier
doi:10.3792/pjaa.92.7

Mathematical Reviews number (MathSciNet)
MR3447743

Zentralblatt MATH identifier
0476.03047

Subjects
Primary: 35P05: General topics in linear spectral theory
Secondary: 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis

Keywords
Schrödinger operators positive eigenvalues von Neumann-Wigner

Citation

Richard, Serge; Uchiyama, Jun; Umeda, Tomio. Schrödinger operators with $n$ positive eigenvalues: an explicit construction involving complex-valued potentials. Proc. Japan Acad. Ser. A Math. Sci. 92 (2016), no. 1, 7--12. doi:10.3792/pjaa.92.7. https://projecteuclid.org/euclid.pja/1451330560


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References

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