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.