How to use the quantum tunnelling probability calculator
Estimate the chance an electron tunnels through a barrier taller than its energy. Enter barrier height above particle energy, barrier width in the fields above; the decay constant kappa, transmission probability are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “quantum tunnelling”, “barrier penetration”, “tunnelling probability”, “calculate quantum tunnelling probability”, “find decay constant kappa”.
Formula
Variables
- dE — Barrier height above particle energy (eV)
- w — Barrier width (nm)
Worked example
With barrier height above particle energy = 1 eV, barrier width = 0.5 nm, the calculator gives decay constant kappa ≈ 5.123167 1/nm; transmission probability ≈ 0.5957125 %.
Frequently asked questions
What is the quantum tunnelling probability calculator used for?
Estimate the chance an electron tunnels through a barrier taller than its energy. It helps with questions such as “quantum tunnelling”, “barrier penetration”, “tunnelling probability”.
What is the formula for the quantum tunnelling probability calculation?
Decay constant kappa (1/nm) = √(2 × ME × dE × QE) / (HPLANCK / (2 × π)) × 1e-9. Transmission probability (%) = 100 × exp(-2 × [Decay constant kappa] × w). Here dE is barrier height above particle energy (eV), w is barrier width (nm).
What inputs do I need for the quantum tunnelling probability calculator?
You need barrier height above particle energy in eV, barrier width in nm. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the quantum tunnelling probability calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the quantum tunnelling probability result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.