Normal-ordered equivalent of the Weyl ordering of $\hat{q}^j \hat{p}^k$
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910032654761984 |
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| author | Lim, Hendry M. |
| author_facet | Lim, Hendry M. |
| contents | The problem of quantizing a bivariate dynamical system can be reduced to evaluating the ordering of $\hat{q}^j \hat{p}^k$. Here, we consider the Weyl ordering of $\hat{q}^j \hat{p}^k$ that is then expressed in term of the annihilation $\hat{a}$ and creation $\hat{a}^\dagger$ operator. The explicit formula for the normal-ordered equivalent (all $\hat{a}^\dagger$'s preceeding all $\hat{a}$'s) of the resulting expression is then given, and some relations are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21538 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Normal-ordered equivalent of the Weyl ordering of $\hat{q}^j \hat{p}^k$ Lim, Hendry M. Mathematical Physics The problem of quantizing a bivariate dynamical system can be reduced to evaluating the ordering of $\hat{q}^j \hat{p}^k$. Here, we consider the Weyl ordering of $\hat{q}^j \hat{p}^k$ that is then expressed in term of the annihilation $\hat{a}$ and creation $\hat{a}^\dagger$ operator. The explicit formula for the normal-ordered equivalent (all $\hat{a}^\dagger$'s preceeding all $\hat{a}$'s) of the resulting expression is then given, and some relations are discussed. |
| title | Normal-ordered equivalent of the Weyl ordering of $\hat{q}^j \hat{p}^k$ |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2602.21538 |