Uploaded June 2025 | Updated September 2026, 1 hour ago
📘 Lesson 20 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
What happens when a quantum particle hits a sudden barrier?
In this lesson, we explore how a quantum particle behaves when it encounters a step potential—a sudden change in potential energy at a single point. You'll learn how to solve the time-independent Schrödinger equation across this discontinuity and apply matching conditions to connect solutions on either side. We analyze two key scenarios: when the particle's energy is lower than the step (revealing the phenomenon of quantum tunneling) and when it is higher than the step (involving partial reflection and transmission). The lesson culminates in a surprising result: even a steep downward drop can fully reflect a quantum particle—a phenomenon known as quantum reflection.
📝 Solved exercises for this course are available here: quantphys.com/lessons/qm1
📘 Lesson 20 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
What happens when a quantum particle hits a sudden barrier?
In this lesson, we explore how a quantum particle behaves when it encounters a step potential—a sudden change in potential energy at a single point. You'll learn how to solve the time-independent Schrödinger equation across this discontinuity and apply matching conditions to connect solutions on either side. We analyze two key scenarios: when the particle's energy is lower than the step (revealing the phenomenon of quantum tunneling) and when it is higher than the step (involving partial reflection and transmission). The lesson culminates in a surprising result: even a steep downward drop can fully reflect a quantum particle—a phenomenon known as quantum reflection.
📝 Solved exercises for this course are available here: quantphys.com/lessons/qm1
![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.")
