Published May 5, 2025
| Version Published
Journal Article
Open
Minimizing Schrödinger eigenvalues for confining potentials
Creators
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1.
Ludwig-Maximilians-Universität München
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2.
California Institute of Technology
Abstract
We consider the problem of minimizing the lowest eigenvalue of the Schrödinger operator −Δ + V in L²(Rd) when the integral ∫e−tV dx is given for some t > 0. We show that the eigenvalue is minimal for the harmonic oscillator and derive a quantitative version of the corresponding inequality.
Copyright and License
Open Access. ©2025 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. © 2025 by the author. This paper may be reproduced, in its entirety, for non-commercial purposes.
Funding
Partial support through US National Science Foundation (DMS-1954995), as well as through the German Research Foundation (EXC-2111-390814868 and TRR 352-470903074) is acknowledged.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2407.15103 (arXiv)
Funding
- National Science Foundation
- DMS-1954995
- Deutsche Forschungsgemeinschaft
- EXC-2111-390814868
- Deutsche Forschungsgemeinschaft
- TRR 352-470903074