Schrödinger operators with a complex valued potential
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- Proc. Amer. Math. Soc. 140 (2012), 4203-4204 Request permission
Abstract:
If $M_n$ is a compact Riemannian manifold for which $H^1(M_n,\mathbb {Z})=0$, $V$ is a continuous complex valued function whose imaginary part is of constant sign, and $-\Delta \psi +V\psi =0$ for some $C^2$ complex valued function $\psi$ on $M_n$, then either $\psi$ vanishes somewhere or there is a constant $c$ and an everywhere positive function $F$ such that $\psi =cF$.References
- K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies, No. 32, Princeton University Press, Princeton, N. J., 1953. MR 0062505
- Sol Schwartzman, Schrödinger operators and the zeros of their eigenfunctions, Comm. Math. Phys. 306 (2011), no. 1, 187–191. MR 2819423, DOI 10.1007/s00220-011-1272-3
Additional Information
- Sol Schwartzman
- Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881
- Email: solschwartzman@gmail.com
- Received by editor(s): May 19, 2011
- Published electronically: April 4, 2012
- Communicated by: Chuu-Lian Terng
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 4203-4204
- MSC (2010): Primary 35J10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11367-X
- MathSciNet review: 2957209