Uploaded June 2025 | Updated September 2026, 1 day ago
📘 Lesson 16 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
What happens when a quantum particle is trapped in a box?
In this lesson, we explore the iconic "particle in a box" problem—a foundational example that illustrates stationary states, quantized energy levels, and wave functions in quantum mechanics. You'll see how solving the Schrödinger equation under simple boundary conditions leads to discrete energy levels and sinusoidal stationary wave functions. We examine how the particle's probability distribution evolves with increasing energy and how this connects to classical behavior. This analytically solvable model reveals deep insights into the nature of quantum confinement and energy quantization.
📝 Solved exercises for this course are available here: quantphys.com/lessons/qm1
📘 Lesson 16 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
What happens when a quantum particle is trapped in a box?
In this lesson, we explore the iconic "particle in a box" problem—a foundational example that illustrates stationary states, quantized energy levels, and wave functions in quantum mechanics. You'll see how solving the Schrödinger equation under simple boundary conditions leads to discrete energy levels and sinusoidal stationary wave functions. We examine how the particle's probability distribution evolves with increasing energy and how this connects to classical behavior. This analytically solvable model reveals deep insights into the nature of quantum confinement and energy quantization.
📝 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.")
![Attractive Potential with No Ground State [QBE Ep. 2]](https://i.ytimg.com/vi/z6HmvZ70S2A/mqdefault.jpg "Attractive Potential with No Ground State [QBE Ep. 2]
Episode 2 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, we explore the strange and fascinating -1/x^2 potential. Despite being attractive and infinitely deep, it has no ground state and therefore no discrete energy spectrum. In a certain regime, the system can be so unstable that it could (theoretically) destroy the universe. No equations just simple dimensional analysis.")
