Symmetries and conserved quantities

  • Thread starter plmokn2
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  • #1
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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
 

Answers and Replies

  • #2
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It should be, because the conservation of angular momentum is from the
rotational invariance of the Hamiltonian.
 
  • #3
Avodyne
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No. Angular momentum is not "momentum along the curve of a circle", but rather [itex]\vec x\times\vec p[/itex]. There is nothing comparable that is conserved for a generic elliptically symmetric potential.
 
  • #4
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I think his 'momentum' here is angular momentum.
If your elliptically symmetric potential is [tex]V(\rho,z)=\frac{1}{\rho^2+\alpha z^2},~\alpha\neq 1[/tex], then angular momentum along axis
'z' is conserved.
 
Last edited:
  • #5
malawi_glenn
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The only thing i can remember know is that in case of an elliptic potential well, J = L + S is not a good quantum number, scince the energy eigenvalues will be "mixed" with same M_J etc, c.f The Nilsson model of Atomic Nucleus.
 
  • #6
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Thanks for your replies, sorry for the slightly ambiguious question.
 
  • #7
blechman
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Angular momentum around the azimuthal direction will still be conserved, but the TOTAL angular momentum will not. This is basically what PRB147 said, but maybe slightly clarified.
 

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