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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2605.24694 |
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| _version_ | 1866917528296488960 |
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| author | Stubbe, Joachim |
| author_facet | Stubbe, Joachim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24694 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sum rules and a second order Feynman-Hellman theorem for abstract operators with applications Stubbe, Joachim Spectral Theory Mathematical Physics 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. |
| title | Sum rules and a second order Feynman-Hellman theorem for abstract operators with applications |
| topic | Spectral Theory Mathematical Physics |
| url | https://arxiv.org/abs/2605.24694 |