Helium wave functions

  • Thread starter MiCasilla
  • Start date

MiCasilla

Does it matter if we use one wave function to describe both electrons of a helium atom, or we need to use one wave function for each? Is there any empirical evidence of the right way?
 
79
0
The Hamiltonian for the system contains a term describing the repulsion of the electrons -- so, to do it properly, you need to consider both electrons at the same time.

As a first approximation, you can assume that this term is negligible. In that case, the Hamiltonian splits into 2 independant hydrogen Hamiltonians (with a nuclear charge of 2e instead of e, of course), and an exact solution can be found. This solution turns out to be a product of hydrogenic wave functions. Since the He atom is just double the number of protons and electrons of H, this makes sense.

To do the analysis properly, we cannot ignore the electron-electron interaction, in which case the math gets messy. A common way to perform the analysis is to use the variational method. This involves using a trial function with adjustable paramaters to get an approximation for the ground state energy. Using more and more complicated functions, the ground state can be approximated extremely well (of course, we know the real value from experiments).
 

Related Threads for: Helium wave functions

  • Posted
Replies
3
Views
2K
  • Posted
Replies
10
Views
4K
  • Posted
Replies
4
Views
879
  • Posted
Replies
3
Views
3K
  • Posted
Replies
23
Views
5K
  • Posted
Replies
1
Views
3K
  • Posted
Replies
2
Views
1K
  • Posted
Replies
4
Views
3K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top