# quantum\_tunnelling

## Basic idea

A particle has nonzero probability of crossing a potential barrier higher than its kinetic energy — classically forbidden, quantum-mechanically routine.

## Key formulas

* Transmission coefficient (rectangular barrier, $E\<V$): $T \approx e^{-2\kappa L}$
* Decay constant inside barrier: $\kappa = \dfrac{\sqrt{2m(V-E)}}{\hbar}$
* WKB approximation: $T \approx \exp!\left(-\dfrac{2}{\hbar}\int\_a^b \sqrt{2m(V(x)-E)},dx\right)$

## Interesting

* Quantum tunelling points to the fact that particles may travel faster than light, see "Hartman effect", <https://www.quantamagazine.org/quantum-tunnel-shows-particles-can-break-the-speed-of-light-20201020/>

### Resources

* <https://www.quantamagazine.org/quantum-tunnel-shows-particles-can-break-the-speed-of-light-20201020/>
* <https://en.wikipedia.org/wiki/Hartman_effect>


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