Symmetry groups of molecule - Hamiltonian

[Konte]

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?

Thanks.
Konte

 

[A. Neumaier]

Yes.

 

[Konte]

Yes.

Thank you for your answer.
Could you please indicate how to demonstrate this (any link or book?)

 

[A. Neumaier]

Thank you for your answer.
Could you please indicate how to demonstrate this (any link or book?)

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.

 

[Konte]

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.

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.

Thanks