Uploaded June 2025 | Updated September 2026, 13 hours ago
📘 Lesson 10 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
How do we quantify uncertainty in quantum mechanics?
In this lesson, you'll learn how to measure the spread of possible outcomes for a quantum observable using the concept of uncertainty. Starting from the basic idea of deviation from the mean, we develop a practical formula involving expectation values. We then apply this to a coherent state of a harmonic oscillator, calculating the uncertainties in position and momentum—and getting our first glimpse of the famous Heisenberg uncertainty principle.
📝 Solved exercises for this course are available here: quantphys.com/lessons/qm1
📘 Lesson 10 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
How do we quantify uncertainty in quantum mechanics?
In this lesson, you'll learn how to measure the spread of possible outcomes for a quantum observable using the concept of uncertainty. Starting from the basic idea of deviation from the mean, we develop a practical formula involving expectation values. We then apply this to a coherent state of a harmonic oscillator, calculating the uncertainties in position and momentum—and getting our first glimpse of the famous Heisenberg uncertainty principle.
📝 Solved exercises for this course are available here: quantphys.com/lessons/qm1
![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.")
