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For a particle moving in Coulomb potential $V(r) = k/r$, using Poisson brackets, show that the Runge Lenz vector $$ \vec{N} = \vec{v}\times\vec{L} - k \vec{r}/r $$ is a constant of motion where $\vec{v}$ is the velocity, and $\vec{L}$ is the angular momentum of the particle.
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4727:Diamond Point
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