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Therefore, we can integrate the identity over the entire โ„๐‘‘: โˆซ โˆฃ โ„๐‘‘ ๐ดฬ‚๐œ“(๐ฑ)โˆฃ2 ๐‘‘๐ฑ = โˆซ โˆฃ ๐œ“(๐ฑ) โ„๐‘‘ โˆฃ2 ๐‘Ž๐‘ค 2 (๐ฑ)๐‘‘๐ฑ + โˆซ (Im[๐œ“โˆ—(๐ฑ)(๐ดฬ‚๐œ“)(๐ฑ)]) 2 โˆฃ ๐œ“(๐ฑ)โˆฃ2 โ„๐‘‘ ๐‘‘๐ฑ

By Lemma A

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Hall's exact variance decomposition in Bohmian Mechanics

quant-ph ยท 2025-12-31 ยท unverdicted ยท novelty 6.0

In Bohmian mechanics Hall's decomposition separates momentum variance into classical dispersion from the guidance field plus a quantum term from amplitude variations, with weak-value real and imaginary parts mapping directly onto the two terms.

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  • Hall's exact variance decomposition in Bohmian Mechanics quant-ph ยท 2025-12-31 ยท unverdicted ยท none ยท ref 3

    In Bohmian mechanics Hall's decomposition separates momentum variance into classical dispersion from the guidance field plus a quantum term from amplitude variations, with weak-value real and imaginary parts mapping directly onto the two terms.