Show that the transformation
$$ \vec{r} \rightarrow \vec{r}^\prime = \vec{r} - m [ 2\dot{\vec{r}} (\vec{\epsilon}\cdot\vec{r}) - \vec{r}(\vec{\epsilon}\cdot\dot{\vec{r}}) (\vec{r}.\dot{\vec{r}}) \vec{\epsilon} ] $$
are symmetry transformations for a particle of mass $m$, moving in Coulomb potential $V(r)= -k/r$. Show that this symmetry implies conservation of Runge Lenz vector $$ \vec{N} = \vec{p}\times \vec{L} - k\, m\, {\vec{r}\over r} $$
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4727:Diamond Point
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