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arXiv · 2508.19783

Canonical pairs in finite-dimensional Hilbert space

Ralph Adrian E. Farrales·Eric A. Galapon
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Abstract

A pair of Hermitian operators is canonical if they satisfy the canonical commutation relation. It has been believed that no such canonical pair exists in finite-dimensional Hilbert space. Here, we obtain canonical pairs by noting that the canonical commutation relation holds in a proper subspace of the Hilbert space. For a given Hilbert space, we study the many possible canonical pairs and look into the uncertainty relation they satisfy. We apply our results by constructing time operators in finite-dimensional quantum mechanics.

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Ralph Adrian E. Farrales, Eric A. Galapon. 2025-08-27. Canonical pairs in finite-dimensional Hilbert space. https://doi.org/10.1016/j.physleta.2026.131344

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