text: The triplet orthohydrogen state has total nuclear spin I = 1 so that the component along a defined axis can have the three values MI = 1, 0, or −1. The corresponding nuclear spin wavefunctions are ,  and . This formalism uses standard bra–ket notation; the symbol ↑ represents the spin-up wavefunction and the symbol ↓ the spin-down wavefunction for a nucleus, so ↑↓ means that the first nucleus is up and the second down. Each orthohydrogen energy level then has a (nuclear) spin degeneracy of three, meaning that it corresponds to three states of the same energy (in the absence of a magnetic field). The singlet parahydrogen state has nuclear spin quantum numbers I = 0 and MI = 0, with wavefunction . Since there is only one possibility, each parahydrogen level has a spin degeneracy of one and is said to be non-degenerate.
  Allowed rotational energy levels
  Since protons have spin , they are fermions and the permutational antisymmetry of the total  wavefunction imposes restrictions on the possible rotational states of the two forms of . Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons, corresponding to odd values of the rotational quantum number J; conversely, parahydrogen with an antisymmetric nuclear spin function, can only have rotational wavefunctions that are symmetric with respect to permutation of the two protons, corresponding to even J.