21. Quantum tunneling

📘 Lesson 21 of 21

▶️ Watch the full lecture series here: https://www.youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv

How can a quantum particle pass through a classically impenetrable wall?

In this final lesson, we explore the iconic quantum phenomenon of tunneling—where a particle with energy lower than a barrier’s height still has a chance of crossing it. Focusing on a rectangular potential barrier, we solve the time-independent Schrödinger equation in three regions and apply matching conditions to determine the full wave function. You’ll see how, even though classical physics forbids it, the quantum particle’s wave packet partially transmits through the barrier. The result is a vivid demonstration of tunneling, one of the most counterintuitive and foundational effects in quantum mechanics.

📝 Solved exercises for this course are available here: https://www.quantphys.com/lessons/qm1