Uploaded June 2025 | Updated September 2026, 20 minutes ago
📘 Lesson 19 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
How does a quantum particle behave in free space, without boundaries?
In this lesson, we develop the quantum mechanical description of a free particle—a system with no confining potential and a continuous range of allowed energies. You'll learn how the general solution to the Schrödinger equation transitions from discrete sums to continuous integrals. We then introduce the Gaussian wave packet, a practical example that illustrates how a free particle moves and spreads over time.
📝 Solved exercises for this course are available here: quantphys.com/lessons/qm1
📘 Lesson 19 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
How does a quantum particle behave in free space, without boundaries?
In this lesson, we develop the quantum mechanical description of a free particle—a system with no confining potential and a continuous range of allowed energies. You'll learn how the general solution to the Schrödinger equation transitions from discrete sums to continuous integrals. We then introduce the Gaussian wave packet, a practical example that illustrates how a free particle moves and spreads over time.
📝 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.")
