⚛️ Quantum Tunnelling (2D)

What It Demonstrates

This is a plain 2D-canvas rendering of a real numerical solve of the 1-D time-dependent Schrödinger equation, using the split-step Fourier method: at every step the wave function is multiplied by the potential phase in position space, Fourier-transformed, multiplied by the exact kinetic-energy phase in momentum space, then transformed back.

• The blue curve is the probability density |ψ(x)|².
• The green curve is the real part of the wave function Re(ψ).
• The yellow bar is the potential barrier V(x).

How to Use

Pick a preset or drag the sliders. Higher/wider barriers and heavier particles suppress transmission; the panel reports the transmission T and reflection R measured by integrating |ψ|² on each side of the barrier once the packet has cleared it.

Did You Know?

The same physics underlies the scanning tunnelling microscope, the tunnel diode, and alpha radioactive decay, where a nucleus's alpha particle leaks through the nuclear Coulomb barrier.

About the 2D Quantum Tunnelling Simulation

This is a plain 2D-canvas version of a real numerical solve of the one-dimensional time-dependent Schrödinger equation for a Gaussian wave packet approaching a rectangular potential barrier. It uses the split-step Fourier method: each time step applies the potential in position space, transforms to momentum space with a fast Fourier transform to apply the kinetic term exactly, then transforms back. The panel reports the measured transmission and reflection coefficients, integrated from the actual |ψ|² distribution once the packet has cleared the barrier.

Quantum tunnelling is the purely quantum phenomenon in which a particle penetrates a barrier higher than its energy, something forbidden in classical mechanics. Transmission probability falls roughly exponentially with barrier height and width and with particle mass — try the presets to see the effect of each.

Frequently Asked Questions