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.

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.

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