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arXiv · 2602.21538

Normal-ordered equivalent of the Weyl ordering of $\hat{q}^j \hat{p}^k$

Hendry M. Lim
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Abstract

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.

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Hendry M. Lim. 2026-02-25. Normal-ordered equivalent of the Weyl ordering of $\hat{q}^j \hat{p}^k$. https://arxiv.org/abs/2602.21538

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