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Quantum tunnelling
Intermediate
Particles cross barriers they classically could not.
T ≈ e^{−2κa}A particle can cross a potential barrier higher than its energy, with probability T ≈ e^{−2κa}, κ = √(2m(V − E))/ħ. It decreases rapidly with width and mass.
Electrons tunnel across 1 nm gaps in electronics.
Not a violation of energy conservation.
In more detail
Quantum tunnelling allows a particle to pass through a potential barrier higher than its energy, with a probability that falls exponentially with barrier width and height.
Real-world uses
- Scanning tunnelling microscopes image individual atoms using tunnelling.
- Flash memory and tunnel diodes depend on tunnelling.
- Engineers use quantum tunnelling in flash memory, where electrons pass through thin insulating layers to store data.
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Frequently asked questions
Does the particle borrow energy?
No such borrowing is needed; the wave description gives a finite probability of transmission.
Why is tunnelling important in practice?
It limits the scaling of microchips, because electrons tunnel through thin insulators.
How can a particle pass through a barrier it lacks energy for?
Its wavefunction is nonzero on the other side, so there is a finite probability of finding it there.
Related topics in Quantum Mechanics
Particle in a box · Free particle · Finite potential well · Tunnelling applications · Alpha decay as tunnelling · Quantum harmonic oscillator