Because the wavefunction of electrons is antisymmetric under exchange, two electrons in the same orbital must take opposite values for this property by the Pauli exclusion principle.
In more than two dimensions, this quantity's namesake group is a universal cover of SO(n). The wavefunction is multiplied by -1 raised to twice this quantity under exchange of identical particles. The first sign of the existence of this property was the (*) splitting of beams of atoms directed through a non-uniform magnetic field. Because the wavefunction of electrons is antisymmetric under exchange, two electrons in the same orbital must take opposite values for this property by the Pauli exclusion principle. All fermions have a half-integer value of this property, and all bosons have an integer value. For 10 points, name this property considered an intrinsic form of angular momentum.
In more than two dimensions, this quantity's namesake group is a universal cover of SO(n).
spin