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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.17830 |
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| _version_ | 1866913807308161024 |
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| author | Kokoulin, Radmir |
| author_facet | Kokoulin, Radmir |
| contents | We introduce a self-adjoint time operator $T_w = i\hbar\bigl(\partial_E + \tfrac12\,\partial_E\ln w(E)\bigr)$ on the weighted energy space $L^2(\mathbb R,\,w(E)\,dE)$. Under mild conditions on the weight $w$ (positivity, local absolute continuity, and uniform bounds at large $\lvert E\rvert$), we prove that $T_w$ is essentially self-adjoint. A simple unitary conjugation carries $T_w$ back to $i\hbar\,\mathrm{d}/\mathrm{d}E$, which in turn leaves the Hamiltonian spectrum unbounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-Adjoint Time Operator in a Weighted Energy Space Kokoulin, Radmir Quantum Physics We introduce a self-adjoint time operator $T_w = i\hbar\bigl(\partial_E + \tfrac12\,\partial_E\ln w(E)\bigr)$ on the weighted energy space $L^2(\mathbb R,\,w(E)\,dE)$. Under mild conditions on the weight $w$ (positivity, local absolute continuity, and uniform bounds at large $\lvert E\rvert$), we prove that $T_w$ is essentially self-adjoint. A simple unitary conjugation carries $T_w$ back to $i\hbar\,\mathrm{d}/\mathrm{d}E$, which in turn leaves the Hamiltonian spectrum unbounded. |
| title | Self-Adjoint Time Operator in a Weighted Energy Space |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.17830 |