z = \frac{z}{H}, ρ = \frac{Σ}{H} ρ (z), p = \frac{P}{H} p (z) .

Using

P = Σ H^{2} Ω_{z}^{2}

\frac{d p}{d z} = - ρ z,

with normalizations

\int ρ d z = 1

and

\int p d z = 1

p = c_{s}^{2} ρ

, and these conventions give the Gaussian distribution

ρ (z) = p (z) = \frac{1}{2 π} e^{- z^{2} /2} .

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