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Ground State Wave function

  1. Apr 1, 2003 #1
    Hi,
    Why is that, the ground state eigenfunction in ANY quantum mechanical system is symmetric under inversion of co-ordinates?
     
  2. jcsd
  3. Apr 1, 2003 #2
    well first of all, this isn t true. the groundstate is only symmetric if the hamiltonian is also symmetric.

    so let s assume that you had asked this question about any quantum system with a symmetric hamiltonian.

    when there is a symmetric hamiltonian, all eigenfuctions must be either even or odd. that is, they must be either symmetric or antisymmetric.

    an antisymmetric wavefunction necessarily passes through zero. therefore it has a node, therefore it cannot be the ground state.

    therefore the ground state must be symmetric.
     
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