Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Quantum Mechanical Tunneling

The phenomenon where a particle can pass through a potential barrier even if it does not have enough energy to overcome it classically.
📜

The statement of the theorem

Consider a particle of mass mm encountering a potential barrier V(x)V(x) defined over x∈[a,b]x \in [a, b], such that E<V(x)E < V(x) in this region. The transmission probability TT through the barrier, derived from the WKB approximation, is given by:\nT≈exp⁡(−2ℏ∫ab2m(V(x)−E) dx)T \approx \exp\left(-\frac{2}{\hbar} \int_{a}^{b} \sqrt{2m(V(x) - E)} \, dx\right)\nwhere EE is the particle's total energy.
Source: Wikipedia