Finding the Hamiltonian for the Be Atom without Nuclear Terms

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Homework Help Overview

The discussion revolves around the formulation of the quantum mechanical Hamiltonian for the beryllium atom, specifically using the Born-Oppenheimer approximation while excluding nuclear terms. Participants are exploring the complexities of many-electron systems in quantum mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the number of electrons in the beryllium atom and the treatment of the nucleus as a point charge. Questions arise regarding the inclusion of electron spins and the starting point for the Hamiltonian formulation.

Discussion Status

The conversation is active, with participants offering insights into the components of the Hamiltonian and the implications of the Born-Oppenheimer approximation. There is acknowledgment of the significant assumptions being made, particularly regarding the neglect of nuclear terms.

Contextual Notes

There is a mention of homework constraints that require the exclusion of certain terms, which some participants recognize as a substantial assumption. The discussion reflects varying interpretations of how to approach the Hamiltonian formulation under these conditions.

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I have a problem that uses the QM Hamiltonian for the berylium atom, but I am having trouble finding this Hamiltonian using the Born-Oppenheimer approximation (leaving out the nuclear-nucler and nucler-electron terms).
Any know how to get this?
 
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It's not difficult. How many electrons does this atom have ? Can you treat the nucleus as a point particle charge ? Are you requires to use the spins of the electrons?

Daniel.

P.S. You can't leave out the nuclear-electron interaction terms.
 
Be has 4 electrons. Yes, they are assumed point charges. Electron spin should be included. Does it start with H=(-ћ2/2m)∑…? That is where I thought I should start, but am stuck after that. I have never seen a Hamiltonian developed for a many-electron atom.
 
You just have to add all possible terms: KE for the 4 electrons, KE for the nucleus, then Coulomb interaction for the 4 electrons among each other , Coulomb interaction for the 4 electrons with the nucleus and finally spin terms: spin-orbit interaction for the electrons and spin-spin interactions for the electrons, that is, of course, if you neglect nuclear spin.

Daniel.
 
Thanks for your help. I think I've got it now. Since I can make the Born-Oppenheimer approximation, I can leave KE for the nucleus out (basically ignore the nucleus all together) which I know is a HUGE assumption to make, but that is what the problem instructs.
 

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