Position representation in quantum mechanics ($\psi (x)=⟨x|\psi ⟩$)

The wavefunction is the probability amplitude of a quantum state in the generalized position basis. For a scalar particle on a line, the position operator multiplies by $x$ and the momentum operator acts as $-i\hslash d/dx$ on their appropriate domains. This makes the canonical commutation relation $[x,p]=i\hslash$ explicit.