Uploaded June 2025 | Updated September 2026, 2 days ago
📘 Lesson 17 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
Where does motion come from in quantum mechanics?
In this lesson, we uncover the origin of motion in quantum systems by exploring superpositions of stationary states. Focusing first on a particle in a box, you'll see how combining the ground and first excited states leads to time-dependent probability densities—evidence of quantum motion. We visualize this oscillatory behavior and explain its connection to energy differences. Extending the concept, we introduce a general method for predicting time evolution by expressing any initial state as a superposition of stationary states.
📝 Solved exercises for this course are available here: quantphys.com/lessons/qm1
📘 Lesson 17 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
Where does motion come from in quantum mechanics?
In this lesson, we uncover the origin of motion in quantum systems by exploring superpositions of stationary states. Focusing first on a particle in a box, you'll see how combining the ground and first excited states leads to time-dependent probability densities—evidence of quantum motion. We visualize this oscillatory behavior and explain its connection to energy differences. Extending the concept, we introduce a general method for predicting time evolution by expressing any initial state as a superposition of stationary states.
📝 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.")
