Graduate What are the quantum numbers used to label helium atom eigenfunctions?

[HomogenousCow]

Are there any results on the structure of the helium atom eigenfunctions? By this I'm referring to the non-perturbative structure of the eigenfunctions, AKA what are the quantum numbers that one would use to label the eigenfunctions?

 

[DrClaude]

I am nit sure what you mean by "non-perturbative," as it is a 3-body problem, hence no analytical solutions.

Using the base Hamiltonian, the quantum numbers you get are those that make up the term symbol, L, S, J, and M_J.

 

[WernerQH]

There are also variational methods. With suitably chosen basis functions you can get quite accurate results -- see for example chapter 3 in "Intermediate Quantum Mechanics" by Bethe and Jackiw.

 

[A. Neumaier]

Are there any results on the structure of the helium atom eigenfunctions? By this I'm referring to the non-perturbative structure of the eigenfunctions, AKA what are the quantum numbers that one would use to label the eigenfunctions?

• Drake, G. W. F., & Van, Z. C., Variational eigenvalues for the S states of helium. Chemical Physics Letters 229 (1994), 486-490.
• Yan, Z. C., & Drake, G. W. F., High precision calculation of fine structure splittings in helium and He-like ions. Physical review letters, 74 (1995), 4791.

 

[akhmeteli]

Are there any results on the structure of the helium atom eigenfunctions? By this I'm referring to the non-perturbative structure of the eigenfunctions, AKA what are the quantum numbers that one would use to label the eigenfunctions?

The following may be relevant: http://www.scholarpedia.org/article/Semiclassical_theory_of_helium_atom