# Symmetries and conserved quantities

I know that if a particle is in a spherically symetric potential its angular momentum will be conserved, but what about if somehow we manage to produce say an elliptically symmetric potential? Will the partical then have a momentum along the curve of the ellipse conserved?
Thanks

It should be, because the conservation of angular momentum is from the
rotational invariance of the Hamiltonian.

Avodyne
No. Angular momentum is not "momentum along the curve of a circle", but rather $\vec x\times\vec p$. There is nothing comparable that is conserved for a generic elliptically symmetric potential.

I think his 'momentum' here is angular momentum.
If your elliptically symmetric potential is $$V(\rho,z)=\frac{1}{\rho^2+\alpha z^2},~\alpha\neq 1$$, then angular momentum along axis
'z' is conserved.

Last edited:
malawi_glenn