- #1

- 397

- 0

I've basically sketched what I would think are the only two realistic candidate solutions for two electrons in a potential well. I basically looked for the simplest solution where the electrons made some kind of effort to stay away from each other and wrote it out as a simple product function. Since the product function wasn't symmetric, I reversed the two electrons and added the two functions together. Standard symmetrization. Then I noticed that the anti-symmetric combination looked like it might have lower energy, in this case, than the symmetric combination. So I've got these two wave functions and I can't see any obvious way to tell which would be the correct ground state.

I also haven't figured out if the spin states have a significant effect on the energy. Of course the symmetric combination would have the singlet spin state and the other combination would have the triplet state. I just don't know if I have to worry about that yet.

I posted my sketches in the other thread. I don't know how to make the thumbnails appear below so I'm just going to put these links in and see if they work. I hope the meaning of the diagrams is obvious:

SYMMETRIC FUNCTION:

https://www.physicsforums.com/attachment.php?attachmentid=24045&d=1267583181

ANTISYMMETRIC FUNCTION:

https://www.physicsforums.com/attachment.php?attachmentid=24046&d=1267585014