Variational method For Helium Atom

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SUMMARY

The variational method applied to the Helium atom reveals that the lowest possible energy occurs when the atomic number z is constrained within the range of 1 to 2. This range is attributed to the probability of an electron being close to one proton, effectively reducing the perceived nuclear charge. The discussion clarifies that z cannot be less than 1, as this would imply both electrons could be located within the nucleus, which is not feasible due to the principles of quantum mechanics and electron behavior.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the variational method in quantum physics
  • Knowledge of atomic structure and electron configuration
  • Concept of effective nuclear charge and electron screening
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  • Research the variational method in quantum mechanics
  • Study effective nuclear charge and its implications in multi-electron atoms
  • Explore quantum mechanical models of the Helium atom
  • Investigate electron behavior in atomic nuclei and implications for atomic theory
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Students and researchers in quantum physics, physicists focusing on atomic structure, and anyone interested in the variational method and its applications in multi-electron systems.

Bishop556
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When using the variational method for the Helium atom, we determine that the lowest possible energy occurs when 1<z<2 where z is the atomic number. My professor elaborated that the number is within this range because there is a probability that the electron may be so close to one of the protons that it appears as if there are only two protons. My question is why can't 0<z<1? Why can't both electrons be located inside the nucleus of the atom? Would it still be possible to distinguish them if they were?
 
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I suppose z is the effective nuclear charge seen by an electron, ie the nuclear charge scrreened by the other electron. This can t be smaller than 1.
 

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