e hard scientist doesis to say that he "stipulates his usage"-that is, he informs youwhat terms are essential to his argument and how he is goingto use them. Such stipulations usually occur at the beginningof the book, in the form of definitions, postulates, axioms, andso forth. Since stipulation of usage is characteristic of thesefields, it has been said that they are like games or have a"game structure."

Axiom (Dynamics). There is a distinguished quantum observable, the Hamil-tonian H. Time evolution of states |ψ(t)〉 ∈ H is given by the Schr ̈odingerequationi~ ddt |ψ(t)〉 = H|ψ(t)〉 (1.1)

Axiom (States). The state of a quantum mechanical system is given by a non-zero vector in a complex vector space H with Hermitian inner product 〈·, ·〉.

Axiom (Quantum observables). The observables of a quantum mechanical sys-tem are given by self-adjoint linear operators on H.