Time-reversal symmetry, Kramers' degeneracy and the algebraic eigenvalue problem

A method is presented whereby time-reversal symmetry may be fully exploited in systems exhibiting Kramers' degeneracy. A basis adapted to time-reversal symmetry, i.e. consisting of Kramers pairs, will be transformed into another of the same structure by symplectic unitary or equivalently, by quaternionic unitary transformations. Only one quaternionic hermitean eigenvalue problem of half the original order has to be solved for each Kramers pair. This leads to a significant reduction of the necessary computational effort.