In the 1940s, a 20-something-year-old grad student named Richard Feynman discovered a new way of thinking about quantum mechanics. It's called the Feynman path integral (or functional integral) approach, and it's become fundamental to the way we think about countless aspects of physics today.

The catch is that path integrals are famously complicated! In this video, I'll show you what exactly the path integral is, how we construct it mathematically, and how to actually evaluate it in the simplest example of a free quantum particle.

We'll begin by reviewing how Feynman's sum-over-histories approach intuitively emerges from the double-slit experiment. Then we'll learn to construct the path integral by a similar limiting procedure to the more familiar construction of an ordinary Riemann integral. Next, we'll explicitly compute the answer for a free particle, and we'll uncover a lesson about the Heisenberg uncertainty principle lurking in the result. Finally, we'll see how Feynman's path integral approach connects back to the more familiar description of quantum mechanics in terms of wavefunctions and the Schrödinger equation.

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