Quantum tunnelling

The packet meets a barrier higher than its central longitudinal kinetic energy.

QPE preset #2

This page describes the phenomenon using the current QPE preset and numerical modules as its primary source.

Physical idea

Tunnelling does not require the particle to “borrow energy”. The wavefunction still satisfies the equation in the classically forbidden region and becomes evanescent; for a finite barrier, a tail reaches the far side and creates a transmitted component.

Key relation. For E<V₀ the wave number inside a simple barrier is imaginary, κ=√(2m(V₀−E))/ħ, and transmission decreases roughly as exp(−2κa) for a thick barrier.

Guided protocol from the preset

With the initial values Ex is smaller than V0, yet part of the probability appears beyond the barrier.

Core experiment. Keep Ex and V0 fixed and change only the width a. PT falls rapidly as a increases.

Compare. Diagnostics shows the numerical packet transmission and the plane-wave prediction at the central energy.

Regime. E_x = p_x²/(2m) < V₀; transmission falls rapidly as a increases.

What to observe and how to study it

Increase barrier width only.
Compare the packet with the plane-wave reference.
Move E close to V₀ and observe the change in sensitivity.

History and experimental status

In 1928 Gamow and, independently, Gurney and Condon used wave mechanics to explain alpha decay. A few decades later tunnelling became a laboratory technology, notably in Esaki tunnel junctions.

Representative physical scale

Representative platform	GaAs-like 2DEG / semiconductor nanostructure
Mapping basis	effective-mass mapping (m*=0.067 m_e)
1 QPE length unit	10 nm
1 QPE time unit	57.9 fs
Energy scale E₀=ħ/T₀	11.4 meV
Equivalent frequency E₀/h	2.75 THz
Note	Representative semiconductor mapping. One 10 nm simulation length unit with m*=0.067 m_e gives a time unit near 57.9 fs; material and confinement details can change the effective mass.

The scale is an order-of-magnitude bridge from QPE dimensionless units to one plausible platform; it does not turn the preset into a quantitative simulation of that specific apparatus.

Essential references

G. Gamow — The Quantum Theory of Nuclear Disintegration (Nature 122, 805 (1928))
L. Esaki — New Phenomenon in Narrow Germanium p-n Junctions (Phys. Rev. 109, 603 (1958))

Continue studying

Open Model & Constraints to see exactly what QPE computes and what is left outside the model. For current live values use Help → Current Experiment → Current Parameters.