Quantum Tunneling — Through the Impossible Wall

1Meeting the wall

Classically, a particle with less energy than the barrier height cannot cross it.

Quantum mechanically, the state is described by a wavefunction, and that wavefunction does not instantly become zero inside the barrier.

Memory image: the wave hits the wall, fades inside it, but does not vanish at once.

Tunneling is not “borrowing energy” or violating energy conservation.

2The tail inside

Inside the classically forbidden region, the wave amplitude decays exponentially.

If the barrier is thin enough, the amplitude on the far side is still nonzero.

A measurement therefore has a finite probability of finding the particle beyond the barrier.

Remember: the barrier suppresses probability; it need not reduce it to zero.

3Why it matters

Tunneling is central to alpha decay, stellar fusion, tunnel diodes and scanning tunneling microscopy.

It can inspire metaphor — but first it is a precise, measurable physical effect.

The particle need not follow a classical trajectory through the wall; the prediction comes from the wavefunction and transmission probability.

Foundational source: Gamow (1928) and standard quantum mechanics.