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Symmetric potential

  1. Aug 16, 2007 #1
    I never learned this in the lectures (maybe I was sleeping), but now I think I finally realized what is the reason that eigenstate solutions of SE with a symmetric potential are either symmetric or antisymmetric. Is the argument this:

    "The Hamiltonian and the space reflection operator commute, therefore they have common eigenstates" ?

    If it is this, can somebody explain me why does a constant potential (which is also symmetric) have plane wave solutions, that are not symmetric or antisymmetric.
  2. jcsd
  3. Aug 16, 2007 #2
    Any quantum particle in a constant potential is in an un-bound state, i.e. a plain plane wave.
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