The classical rule, and how quantum mechanics breaks it

Imagine rolling a ball toward a hill. If the ball doesn’t have enough kinetic energy to reach the top, classical physics says it simply rolls back down — there’s no way it ends up on the other side. This is true for everyday objects without exception.

But for particles governed by quantum mechanics — electrons, protons, and other subatomic particles — the rules are different. A particle’s behavior is described by a wavefunction (covered in the Learn topic on quantum superposition), and that wavefunction doesn’t drop to exactly zero the instant it hits a barrier it doesn’t have enough energy to climb over. Instead, it decays exponentially inside the barrier — meaning there’s a small but genuinely nonzero chance the particle appears on the other side, without ever having the energy to go “over” it. This is quantum tunneling.

Wave hits the barrier Fades inside, but not to zero Barrier Small chance of appearing here
A particle's wave doesn't stop dead at a barrier. It fades inside, and if the barrier is thin enough, a smaller wave comes out the other side. That leftover wave is the chance of finding the particle there. (Not to scale.)

Why “tunneling” is a slightly misleading name

The particle doesn’t dig a tunnel or pass through some hidden path — it’s more accurate to say its wavefunction extends into and through the barrier, and there’s a real probability of detecting the particle on the far side if you measure. The narrower and lower the barrier, the higher that probability.

Where tunneling actually matters, not just theoretically

  • The Sun’s fusion: protons in the Sun’s core don’t individually have enough energy to overcome their mutual electric repulsion and fuse, according to classical physics alone — quantum tunneling is what allows fusion to happen at the rate it does, and is part of why stars shine at all.
  • Scanning tunneling microscopes: these instruments image individual atoms on a surface by measuring a tunneling current between a sharp tip and the surface, sensitive to distances smaller than the width of an atom.
  • Radioactive alpha decay: some unstable atomic nuclei emit particles via tunneling, escaping a nuclear “wall” they wouldn’t classically have enough energy to overcome.
  • Flash memory and some transistors: modern computer chips rely on tunneling effects, both as something to exploit and something to carefully manage as components shrink to atomic scales.

Why this matters

Quantum tunneling is a genuinely strange effect with enormous real-world consequences — it’s part of why the Sun burns, why some electronics work the way they do, and a clear demonstration that at small enough scales, “possible” and “impossible” aren’t as sharply separated as classical physics would have you believe.