Next, take a Hamiltonian invariant under T. Let |a⟩ and T|a⟩ be two quantum states of the same energy. Now, if , then one finds that the states are orthogonal: a result called Kramers' theorem. This implies that if , 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.
Next take a Hamiltonian invariant under T. Let |a⟩ and T|a⟩ be two quantum states of the same energy. Now, if , then one finds that the states are orthogonal: a result called Kramers' theorem. This implies that if , 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.