A free Gaussian wavepacket evolves under the Schrödinger equation. Position measurement collapses the superposition to a narrow packet near the observed position, with probability |ψ(x)|².
iℏ ∂ψ/∂t = −(ℏ²/2m)∂²ψ/∂x² + V(x)ψ · Collapse: ψ → δ(x−x_obs) / Born rule: P(x) = |ψ(x)|²