Complete Quantum Mechanics

States

A quantum state is represented by a vector $|\psi\rangle$ or wavefunction $\psi(x)$.

Dynamics

Time evolution is governed by

$$i\hbar\frac{\partial}{\partial t}|\psi\rangle = H|\psi\rangle.$$

Operators

Observables are operators. Noncommutativity is encoded in commutators such as $[\hat x,\hat p]=i\hbar$.