A theory stating that the energy levels of a system, such as an atom that contains an odd number of spin-½‎ particles (e.g. electrons), are at least double degenerate in the absence of an external magnetic field. This degeneracy, known as the Kramers degeneracy, is a consequence of time reversal invariance. The Kramers theorem was stated by Hendrik Anthony Kramers in 1930. Kramers degeneracy is removed by placing the system in an external magnetic field. The splitting of energy levels that occurs when this is done is very useful in the application of electron paramagnetic resonance to ions of transition elements. The theorem holds even in the presence of crystal fields (see crystal-field theory) and spin–orbit coupling.