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.
The set {𝐱:∣ 𝜓(𝐱)∣ = 0} = 𝒩 is a Lebesgue null set (by assumption (H5), it has measure zero)
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Hall's exact variance decomposition in Bohmian Mechanics
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.