20. Step potential

📘 Lesson 20 of 21

▶️ Watch the full lecture series here: https://www.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: https://www.quantphys.com/lessons/qm1