Helium ground state questions

Click For Summary
SUMMARY

The ground state configuration of helium is characterized by a wavefunction that is the product of two hydrogenic 1s wavefunctions and a spin eigenstate in a singlet state. The space wavefunction is hydrogenic due to the similar potential experienced by the electrons, which is scaled for the presence of two protons in the nucleus. The necessity for an antisymmetric wavefunction arises from the fermionic nature of electrons, leading to the requirement that the spin component must be in a singlet state to satisfy the antisymmetry condition.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically wavefunctions
  • Familiarity with hydrogenic wavefunctions and their properties
  • Knowledge of fermions and the Pauli exclusion principle
  • Basic concepts of spin states in quantum mechanics
NEXT STEPS
  • Study the properties of hydrogenic wavefunctions in detail
  • Explore the implications of the Pauli exclusion principle on multi-electron systems
  • Learn about antisymmetry in quantum mechanics and its effects on wavefunctions
  • Investigate numerical methods for evaluating multi-electron systems in quantum mechanics
USEFUL FOR

Students and professionals in quantum mechanics, physicists studying atomic structure, and anyone interested in the behavior of multi-electron systems in quantum theory.

spaghetti3451
Messages
1,311
Reaction score
31
I have having difficulty understanding why the ground state configuration of helium has a wavefunction that is the product of two hydrogenic 1s wavefunctions and the spin eigenstate of a singlet state.

Firstly, why is the space wavefcn hydrogenic,
and secondly, why is the spin wavefcn a singlet state?
 
Physics news on Phys.org
If you neglect electron-electron interaction, you have the same potential as in the hydrogen atom - just scaled to account for the second proton in the nucleus. And if you evaluate the system numerically, it turns out that the approximation is not so bad.

As electrons are fermions, the wave-function has to be antisymmetric under the exchange of the two electrons. This is not possible with the space-like part of their wave functions - they both have the same state! Therefore, the spins have to be antisymmetric, which requires a singlet state.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 12 ·
Replies
12
Views
2K
Replies
2
Views
2K