Quantum Tunnelling Probability
Lesson notes
Overview
Barrier penetration falls exponentially with thickness. This topic is rated advanced and is number 213 of 227 in Physics. Deeper models, formal results and harder reasoning.
What you are seeing
The panel above shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.
In depth
Quantum particles can pass through a barrier that classical physics would forbid, because the wave function decays but does not vanish inside the barrier. The transmission probability falls roughly exponentially with the thickness, T ≈ e^(−2κL). Tunnelling makes alpha decay possible, allows fusion in the Sun at temperatures lower than classical theory requires, and underlies flash memory and the scanning tunnelling microscope, which can image single atoms.
Reading the relationship
The expression "T ≈ e^(−2κL)" is a compact summary of the idea. It uses the symbols T, e, κ, L; name what each one stands for before you start. Notice that it contains an exponential, which changes by the same factor for every equal step. Then use the sliders to see how changing one quantity changes the others.
A guided exploration
1. Set every slider to its middle value and note the shape of the curve. 2. Move one slider at a time and describe whether the curve shifts, stretches or turns. 3. Find the value where the behaviour changes sharply, then connect it to the formula.
Try this
Try to explain why the pattern holds, not just what it is. Look for limiting cases and what happens at the edges.
Common pitfalls
Check units and directions first. Many mistakes come from mixing up a scalar with a vector, or from using a formula outside the conditions where it holds.
How it connects
It builds on “Quantised Energy Levels of Hydrogen”, the topic before it in Physics. Once you are comfortable, continue with “Activity of a Radioactive Source”.
Why it matters
Physics explains how the world moves, heats, shines and interacts, and the same principles power technology around you.
Where you might use it
- Revising “Quantum Tunnelling Probability” before a class, exam or certification
- Designing vehicles, bridges and devices where motion, forces or waves must be predicted
- Understanding how sensors, lasers and communication links actually work
- Explaining everyday phenomena such as sound, light, heat and orbits
Frequently asked questions
What is Quantum Tunnelling Probability?
Barrier penetration falls exponentially with thickness. It is an advanced topic in Physics.
How do I use the Quantum Tunnelling Probability simulation?
The panel at the top shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression T ≈ e^(−2κL) packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Deeper models, formal results and harder reasoning. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “Quantised Energy Levels of Hydrogen”, the previous topic in Physics. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.