Most quantum mechanics texts include a phrase such as 'any ket can be written as a sum of eigenkets of a given observable'.
I have problems with the generalities of any ket.
Does this literally mean any ket, or does it mean any ket of the same observable? It seems odd that any ket, say an eigenket of position, should be expressible as a sum of eigenkets of a different observable?
Edit: Unless of course a general state is dependent on more than one summation of eigenkets of more than one observable, but the measurement of one of those observables does not depend on the other summations.