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

HomogenousCow
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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?
 
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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 MJ.
 
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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.
 
HomogenousCow said:
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.
 
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HomogenousCow said:
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
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
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