book viewer 1d 2d spin people glossary about 01 Scene 5 i Free particle No potential. The packet spreads as it moves — Heisenberg uncertainty in action. ii Tunnel barrier A classically impassable wall. Yet some amplitude leaks through — quantum tunneling. iii Double slit Two narrow openings. The packet passes both at once, producing interference fringes downstream. iv Harmonic trap A parabolic bowl. The packet bounces like a pendulum without losing shape — a coherent state. v Circular ring Confined to a closed loop. Boundary conditions force the momentum to take quantized values. ¶
Each scene starts the same Gaussian packet in a different
environment. The split-step Fourier method alternates a half
kinetic step in momentum space with a full potential step in
position space (Strang splitting, O(dt 2 ) );
accuracy holds while the norm ‖ψ‖ stays near unity
— watch the readout under the figure.