  In the following, we will presuppose some familiarity with elementary QM notions like ‘state’, ‘observable’, ‘value’ and their mathematical representatives ‘vector’, ‘(self-adjoint) operator’ and ‘eigenvalue’ [see the entry on  quantum mechanics  for details]. We will usually identify the observables and the operators on an appropriate Hilbert space which represent them; if there is a need to distinguish operators and observables, we write the operators underlined and in boldface. (Thus an operator A represents an observable A.)