[Wien] Is there an effect of SO on the ground state

[pieper]

My 2 cents to this: Not a particularly meaningful question.

The only meaningful thing about energies, as in eigenvalues of the 
Hamiltonian, is their DIFFERENCE. The evolution with time of the state 
of an isokated quantum system (Schrödinger picture) is completely 
governed by the differences of the eigenvalues of the Hamiltonian. The 
choice of where you put zero is up to you.

A common choice for zero is the ground state energy of the Hamiltonian. 
In this case clearly zero is zero, there is no effect of SO.

Other choices are more practical in various circumstances: The mean of 
the spektrum of the Hamiltonian, or the Fermi energy (definition 
discussed recently here), or some fictitious reference limit like the 
state with all charges at infinite distance ... The ground state energy 
then probably will depend on whether or not you put SO into your 
Hamiltonian. After all you consider SO because it changes energy 
differences and might split degeneracies.


---
Dr. Martin Pieper
Karl-Franzens University
Institute of Physics
Universitätsplatz 5
A-8010 Graz
Austria
Tel.: +43-(0)316-380-8564


Am 29.10.2016 23:20, schrieb Abderrahmane Reggad:
> Hello again
> 
> I am waiting for an answer to my question .
> 
> My question is about the effect of the inclusion of the Spin-Orbit
> Coupling on the ground state energy. 
> 
> I want to know if the SO affect the ground state energy also or It
> only causes the splitting of the degenerate state energies.
> 
> Any information will be fruitful for me.
> 
> I hope find an answer to my question
> 
> --
> 
> Mr:
> A.Reggad                                          
> 
> Laboratoire de Génie Physique
> Université Ibn Khaldoun - Tiaret
> 
> Algerie
> 
> 
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