Hamiltonian with Energy Levels Corresponding to Riemann Zeros
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908731507212288 |
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| author | Suo, Xingpao |
| author_facet | Suo, Xingpao |
| contents | A Hamiltonian with eigenenergy \( E_n = ρ_n(1 - ρ_n) \) has been constructed, where \( ρ_n \) denotes the \( n \)-th non-trivial zero of the Riemann zeta function. To construct such a Hamiltonian, we generalize the Berry-Keating paradigm and encode number-theoretic information into the Hamiltonian using modular forms.Although our construction does not resolve the Hilbert-Pólya conjecture (since the eigenstates corresponding to \( E_n \) are \emph{not} normalizable), it provides a novel physical perspective on the Riemann Hypothesis (RH). In particular, we propose a physical interpretation of RH, which could offer a potential pathway toward its proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21192 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamiltonian with Energy Levels Corresponding to Riemann Zeros Suo, Xingpao Quantum Physics Mathematical Physics A Hamiltonian with eigenenergy \( E_n = ρ_n(1 - ρ_n) \) has been constructed, where \( ρ_n \) denotes the \( n \)-th non-trivial zero of the Riemann zeta function. To construct such a Hamiltonian, we generalize the Berry-Keating paradigm and encode number-theoretic information into the Hamiltonian using modular forms.Although our construction does not resolve the Hilbert-Pólya conjecture (since the eigenstates corresponding to \( E_n \) are \emph{not} normalizable), it provides a novel physical perspective on the Riemann Hypothesis (RH). In particular, we propose a physical interpretation of RH, which could offer a potential pathway toward its proof. |
| title | Hamiltonian with Energy Levels Corresponding to Riemann Zeros |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2505.21192 |