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Phase velocity and group velocity

For a dispersion relation

ω (k)

, the phase velocity is

c_{p} = ω / k

and the group velocity is

c_{g} = d ω / d k

. For the Klein-Gordon relation at

k > 0

,

c_{p} = c \frac{k ^{2} + A ^{2}}{k} > c, c_{g} = c \frac{k}{k ^{2} + A ^{2}} < c, c_{p} c_{g} = c^{2} .

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