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Puzzles about the ''groud state manifold''

  1. Mar 1, 2008 #1
    in atomic physics, sometimes one would encounter the termilogy ''ground state manifold''

    my question is, the ground state of an atom is usually unique

    How come the ''ground state manifold''?

    It means several nearly degenerate level?

    are these level stable?
  2. jcsd
  3. Mar 1, 2008 #2
    I think you are referring to the spontaneous breakdown of symmetry, right ?

    Let's take the example of a ferromagnet. This magnet can be composed out of a gazzillion of iron atoms. Each iron atom will interact with its nearest neighbors by aligning its spin along the direction of the neighbor. This lowers their interaction energy. The lowest possible energy wil be reached once all spins have the same direction. Now, different ground state manifolds means that the system can have different physical ststaes that correspond to the lowest energy state. In our example, the lowest energy corresponds to that system which has all its spins aligned into one direction. But, this direction can be up, down, left, right, in between left and right, etc etc. So there are many possible directions ! Again, what matters is that all spins are aligned ! But the direction of those spins can vary from one system to another. This makes that there are many ground states possible !

  4. Mar 1, 2008 #3
    no, it has nothing to do with symmetry spontaneous breaking

    the manifold usually consists of just finite levels

    they may all belong to the l=2 subspace, so the dimension is just 5.

    thanks for your interests anyway.
  5. Mar 1, 2008 #4
    But then what are you asking about ? Ground state manifold just means ground state energy level, that's it.

  6. Mar 2, 2008 #5
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    you are a handsome guy!
  7. Mar 2, 2008 #6


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    well... for example, the ground state of a H-atom is doubly degenerate due to electron spin.
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