In the presence of CP violation, the effective Hamiltonian matrix describing
a neutral meson anti-meson system does not commute with its hermitian
conjugate. As a result, this matrix cannot be diagonalized by a unitary
transformation and one needs to introduce a reciprocal basis. Although known,
this fact is seldom discussed and almost never used. Here, we use this concept
to highlight a parametrization of the Hamiltonian matrix in terms of physical
observables, and we show that using it reduces a number of long and tedious
derivations into simple matrix multiplications. These results have a
straightforward application for propagation in matter. We also comment on the
(mathematical) relation with neutrino oscillations.Comment: 15 pages, no figure
