Quantum Tunneling Simulation

⚛ Quantum Tunneling

Preset Wave Packet Energy (eV) 2.0 Width σ (nm) 0.6 Barrier Height V₀ (eV) 3.0 Width d (nm) 0.5 Position x₀ (nm) 5

Results

Transmission T—

Reflection R—

Classical T—

Step0

|ψ|²

Re(ψ)

V(x)

What It Demonstrates

Quantum tunneling occurs when a particle crosses a potential barrier that it classically could not surmount. This simulation solves the 1-D time-dependent Schrödinger equation using the split-step Fourier method — one of the most efficient algorithms for quantum wave-packet propagation.

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

How to Use

Select a preset, then press Start. Drag sliders to change barrier height V₀ and width d, or wave-packet energy and width. Reset reinitialises the Gaussian wave packet to the left of the barrier.

Did You Know?

Quantum tunneling powers many real devices: the tunnel diode, scanning tunnelling microscope (STM), and nuclear fusion in stars (protons tunnel through the Coulomb barrier at temperatures far below classical threshold). Alpha radioactive decay is also a tunneling process — the alpha particle leaks through the nuclear potential barrier.