Page "Spin isomers of hydrogen" Paragraph 8

Since protons have spin 1 / 2, they are fermions and the permutational antisymmetry of the total H < sub > 2 </ sub > wavefunction imposes restrictions on the possible rotational states the two forms of H < sub > 2 </ sub > can adopt.

Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons.

Conversely, parahydrogen with an antisymmetric nuclear spin function, can only have rotational wavefunctions that are symmetric with respect to permutation of the two protons.

Applying the rigid rotor approximation, the energies and degeneracies of the rotational states are given by