





















Abstract:We discuss the role of the Feynman-Hellmann theorem for abstract one-parameter families of Hamiltonians in sum rules and trace identities of Harrell and the author and its application to spectral theory. In particular, we derive a sum rule for the second derivative of eigenvalues of a one-parameter family of Hamiltonians extending thereby concepts of second order perturbation theory. We present applications to semiclassical eigenvalue bounds of Schrodinger operators as Lieb-Thirring inequalities, zeros of Bessel functions, eigenvalue inequalities for sums of matrices and trace inequalities.
| Comments: | 29 pages |
| Subjects: | Spectral Theory (math.SP); Mathematical Physics (math-ph) |
| Cite as: | arXiv:2605.24694 [math.SP] |
| (or arXiv:2605.24694v1 [math.SP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24694 arXiv-issued DOI via DataCite (pending registration) |
From: Stubbe Joachim [view email]
[v1]
Sat, 23 May 2026 18:14:09 UTC (26 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。