INSTRUMENT 06 / QUANTUM SKETCHBOOK
Wave packets in
potential landscapes.
A one-dimensional quantum laboratory. Shape potential energy and watch probability behave as a wave—reflecting, interfering, tunneling, and spreading.
WAVEFUNCTION ψ(x,t)YELLOW |ψ|² · TEAL Re(ψ) · RED V(x)
320 COMPLEX AMPLITUDES · RK40.00 ms/frame
How can a particle cross a barrier it cannot classically climb?
REPRESENTATIVE EQUATIONiℏ ∂ψ/∂t = −(ℏ²/2m)∂²ψ/∂x² + Vψ
The wave packet splits: one part reflects while a smaller part continues beyond the barrier. The thing evolving is the complex probability amplitude ψ. Its phase controls interference, while |ψ|² gives the probability density that can be measured. The red landscape is potential energy, not a physical wall.
The model samples the Schrödinger equation four times for each Runge–Kutta step, then corrects tiny floating-point drift by renormalizing the total probability to one. That correction keeps the bookkeeping honest without deciding where the particle “really is.”