19. Free particle

📘 Lesson 19 of 21

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