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Symmetry groups of molecule - Hamiltonian

  1. Feb 11, 2016 #1
    Hello everybody,

    As I mentioned in the title, it is about molecular symmetry and its Hamiltonian.
    My question is simple:
    For any molecule that belong to a precise point symmetry group. Is the Hamiltonian of this molecule commute with all the symmetry element of its point symmetry group?

  2. jcsd
  3. Feb 11, 2016 #2

    A. Neumaier

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  4. Feb 11, 2016 #3
    Thank you for your answer.
    Could you please indicate how to demonstrate this (any link or book?)
  5. Feb 11, 2016 #4

    A. Neumaier

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    I don't know of a reference. This is more or less by definition, because atoms with the same number of protons and neutrons are indistinguishable. If you use a second-quantized formulation, you cannot create Hamiltonians where this fails.

    In practice one uses first-quantized formulations only and enforces this through how the molecular force field is set up - by imposing identical coefficients on terms that differ only by a permutation.
    Last edited: Feb 11, 2016
  6. Feb 11, 2016 #5
    Many thanks anyway. In fact, I suspect that the answer is "yes" , so you reassure me largely.
    I turn to somebody who can indicate any demonstration if possible please.

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