Uploaded June 2025 | Updated September 2026, 1 day ago
📘 Lesson 11 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
In this lesson, we explore one of the most iconic results in quantum mechanics: Heisenberg's uncertainty principle. You'll learn why there's a fundamental limit to how precisely we can know a particle's position and momentum at the same time. We then walk through the key steps of a mathematical proof, showing that this limit—the product of uncertainties—can never fall below ℏ⁄2. This principle isn't about measurement limitations; it's a fundamental property of quantum systems.
📝 Solved exercises for this course are available here: quantphys.com/lessons/qm1
📘 Lesson 11 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
In this lesson, we explore one of the most iconic results in quantum mechanics: Heisenberg's uncertainty principle. You'll learn why there's a fundamental limit to how precisely we can know a particle's position and momentum at the same time. We then walk through the key steps of a mathematical proof, showing that this limit—the product of uncertainties—can never fall below ℏ⁄2. This principle isn't about measurement limitations; it's a fundamental property of quantum systems.
📝 Solved exercises for this course are available here: quantphys.com/lessons/qm1
![Quantum Fractals [QBE Ep. 3]](https://i.ytimg.com/vi/_iHbpTirOS4/mqdefault.jpg "Quantum Fractals [QBE Ep. 3]
Episode 3 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 quantum fractals through one of the simplest quantum-mechanical systems: the particle in a box. The fractal wave function discussed here is based on the paper: M. V. Berry, Quantum fractals in boxes, J. Phys. A: Math. Gen. 29, 6617 (1996).")
![Quantum Zeno Effect [QBE Ep. 4]](https://i.ytimg.com/vi/lgYDb7gKhKM/mqdefault.jpg "Quantum Zeno Effect [QBE Ep. 4]
Episode 4 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 how frequent observations more precisely, projective measurements can dramatically alter the time evolution of a quantum system, and in some cases even freeze it altogether. This fascinating phenomenon is known as the quantum Zeno effect.")
![Spontaneous Singularities [QBE Ep. 1]](https://i.ytimg.com/vi/oNhus9iAyys/mqdefault.jpg "Spontaneous Singularities [QBE Ep. 1]
Episode 1 of Quantum on the Back of an Envelope [QBE].
🔗 Watch the full series here: https://www.youtube.com/playlist?list=PLIGRVb L3EpDzApE5EnAOYyTAyagvi1W
In this first episode of Quantum on the Back of an Envelope, we explore an unexpected phenomenon in quantum mechanics: how a perfectly smooth wave function, evolving under the Schrödinger equation, can spontaneously develop a singularity over time.")
