F I q ≡ 4 ( ∇ → a ) 2 Thus, the Lagrangian density of the Madelung flow can be written as: (45) L = − [ ∂ ν ^ ∂ t + 1 2 ( ∇ → ν ^ − k A → ) 2 + k φ ] ρ ^ − ħ 2 8 m F I q The pre-factor ħ 2 8 m seems to appear in every case in which Fisher information appears in a quantum Lagrangian and may be significant.
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