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Symmetries and conserved quantities

  1. Dec 14, 2007 #1
    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
     
  2. jcsd
  3. Dec 14, 2007 #2
    It should be, because the conservation of angular momentum is from the
    rotational invariance of the Hamiltonian.
     
  4. Dec 14, 2007 #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.
     
  5. Dec 14, 2007 #4
    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: Dec 14, 2007
  6. Dec 15, 2007 #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.
     
  7. Dec 15, 2007 #6
    Thanks for your replies, sorry for the slightly ambiguious question.
     
  8. Dec 20, 2007 #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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