SPIN AND THE PAULI
PRINCIPLE
Textbooks sometimes call this
“The Pauli Principle,” or “The Exclusion Principle.” No two
identical fermions can occupy the same state in the same region
of space.
![](data:image/png;base64,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)
Effect of the quantization of
the Coulomb field on the hydrogen spectrum... aka the Lamb
Shift.
NEXT
Back