 The following formula shows that it is "always" possible to write the density matrix in this diagonal form without appealing to operator orderings using the inversion (given here for a single mode),
where and are the amplitude and phase of .Though this is a full formal solution of this possibility, it requires infinitely many derivatives of Dirac delta functions, far beyond the reach of any ordinary tempered distribution theory.If the quantum system has a classical analog, e.g.