Next, take a Hamiltonian invariant under T. Let | a ⟩ and T | a ⟩ be two quantum states of the same energy. Now, if T = −1, then one finds that the states are orthogonal: a result called Kramers' theorem. This implies that if T = −1, then there is a twofold degeneracy in the state. This result in non-relativistic quantum mechanics presages the spin statistics theorem of quantum field theory.