Why Use Product Type Wave Functions for Helium Atom?

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SUMMARY

The discussion focuses on the use of product type wave functions for the helium atom, emphasizing the necessity of accounting for electron-electron repulsion and the importance of anti-symmetry in wave functions. The anti-symmetry is achieved by interchanging the coordinates of the electrons, which is crucial for accurately representing their spins. The selection criteria for the best wave function involve ensuring that it reflects the true ground state energy, which is approximately -77.5 eV, as opposed to an incorrect estimate of -100 eV when electron repulsion is neglected.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of wave functions and anti-symmetry
  • Knowledge of electron correlation in multi-electron systems
  • Familiarity with helium atom properties
NEXT STEPS
  • Study the principles of quantum mechanics related to multi-electron atoms
  • Research the role of anti-symmetry in fermionic systems
  • Explore methods for calculating electron correlation in helium
  • Examine the implications of electron-electron repulsion on atomic energy levels
USEFUL FOR

Physicists, quantum chemists, and students studying atomic structure and electron interactions will benefit from this discussion.

Flava1000
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1. Considering the helium atom,
a. why do we use product type wave function
b. how is the anti-symmetry taking care
c what are the criterion for selecting best wave function
d. how do we take into account the electron correlation



Attempts:
a. I think it is because we want exact wave function, since the helium atom has two electron, the electron-electron repulsion must be ignored.

b. Anti symmetry is taking care by interchanging the coordinates of the electrons
 
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a) The electron-electron repulsion should not be ignored! In fact, I think the energy of the ground state would be around -100 eV if you ignore it while the experimental ground state energy is -77.5 eV.

b) It has to do with the electrons. Think about spins.
 

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