Uploaded June 2025 | Updated September 2026, 36 minutes ago
📘 Lesson 21 of 21
▶️ Watch the full lecture series here: 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: quantphys.com/lessons/qm1
📘 Lesson 21 of 21
▶️ Watch the full lecture series here: 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: quantphys.com/lessons/qm1
![Do Wave Functions Vanish at Infinity? [QBE Ep. 5]](https://i.ytimg.com/vi/t8x4Kw11c80/mqdefault.jpg "Do Wave Functions Vanish at Infinity? [QBE Ep. 5]
Episode 5 of Quantum on the Back of an Envelope [QBE].
🔗 Watch the full series here: https://www.youtube.com/playlist?list=PLIGRVb L3EpDzApE5EnAOYyTAyagvi1W
In this episode of Quantum on the Back of an Envelope, In this episode of Quantum on the Back of an Envelope, we ask whether a quantum mechanical wave function really has to vanish at infinity — an assumption often made in introductory textbooks and courses. To explore this, we examine a specific example (taken from Principles of Advanced Mathematical Physics by Robert D. Richtmyer) of a wave function that is perfectly continuous, differentiable, and normalizable, yet not only refuses to vanish, but actually becomes unbounded at infinity.")
