4 Matching Annotations
 Feb 2023

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 physics/mathematics  Classical Physics  Quantum Mechanics <br /> <br />  State Space  fields satisfying equations of laws<br> the state is given by a point in the space  vector in a complex vector space with a Hermitian inner product (wavefunctions) <br />  Observables  functions of fields<br> usually differential equations with realvalued solutions  selfadjoint linear operators on the state space<br> some confusion may result when operators don't commute; there are usually no simple (realvalued) numerical solutions 



Principle (Observables). States for which the value of an observable can becharacterized by a welldefined number are the states that are eigenvectors forthe corresponding selfadjoint operator. The value of the observable in such astate will be a real number, the eigenvalue of the operator.
What does he mean precisely by "principle"?

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

Axiom (Quantum observables). The observables of a quantum mechanical system are given by selfadjoint linear operators on H.
