The idea of a Fermi hole
requires some background in the idea of anti-symmetrized wavefunctions. The Pauli exclusion principle
is the "rule" that no more than two electrons can be in the same orbital. The "rule" traces to a deep algebraic property of nature that has nothing whatsoever to do with the charge on electrons. The essence is that many-electron wave function
must change sign when the labels on any two electrons are interchanged. This property is called antisymmetry
, and its essential consequence is that electrons either stay out of one another's way, forming what is called a Fermi
hole, or clump together, forming what is called a Fermi
heap. Since electrons repel one another electrically, Fermi holes and Fermi heaps have drastic effects on the energy of many-electron atoms.
It is useful to consider an excited state of the helium atom in which electron 1 is in the 1s orbital and electron 2 has been excited to the 2s orbital. It is not possible, in principle, to distinguish electron 1 from electron 2. In other words, electron 2 might be in the 1s orbital with electron 1 in the 2s orbital. While there are 4 possible spin
states for this system, only the ones in which the spins of both electrons are aligned (pointing in the same direction) will be considered. (This is the triplet state, there exists a singlet state with the spins paired).
Because electrons are fermions
, they must be antisymmetric with respect to exchange. This means that if... Read More