= Solution
The <postulates of quantum mechanics> assign a pure state to a normalized ray in a complex <Hilbert space>, and an observable to a <self-adjoint operator>. A spectral outcome projector $P_a$ has <Born rule> <probability> $p_a=\langle\psi|P_a|\psi\rangle$. An ideal <projective measurement> updates the state to $P_a|\psi\rangle/\sqrt{p_a}$ when $p_a>0$; degeneracy requires the full outcome projector.
Between measurements, an isolated system obeys $i\hbar\partial_t|\psi\rangle=H|\psi\rangle$, giving unitary evolution. Composite systems use <tensor products>; identical particles additionally obey the appropriate exchange symmetry. Mixed preparations use a <density matrix>, with $p_a=\operatorname{tr}(\rho P_a)$. These postulates require a specified <Hamiltonian> and measurement model; they do not assign those automatically.<Quantum Mechanics by David Tong>[Quantum states, observables, measurement and Schrödinger evolution]{ref}
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