Asked by Alice
                Write the Hamiltonian operator for 2 electrons in a 1D box of length a.
I know that the Hamitonian is a sum of the kinetic and potential energies. I was thinking that for 2 electrons in a 1D box it would be:
-2((hbar^2)/2m_e)(d^2/dx^2)) + Coulomb interaction for 2 electrons
I am a bit confused because I don't seem to be using the length of the box anywhere in this.
            
        I know that the Hamitonian is a sum of the kinetic and potential energies. I was thinking that for 2 electrons in a 1D box it would be:
-2((hbar^2)/2m_e)(d^2/dx^2)) + Coulomb interaction for 2 electrons
I am a bit confused because I don't seem to be using the length of the box anywhere in this.
Answers
                    Answered by
            drwls
            
    The box size enters in when writing the potential V(x). It becomes infinite at the ends. There is an interaction potential, but a more important consequence of having two electrons is the Pauli exclusion principle. See the discussion at
http://galileo.phys.virginia.edu/classes/252/symmetry/Symmetry.html
In that discussion, the interaction potential is neglected.
    
http://galileo.phys.virginia.edu/classes/252/symmetry/Symmetry.html
In that discussion, the interaction potential is neglected.
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