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Feynman's (almost) impossible integral

Compute the Feynman path integral and discover the key to quantum mechanics! 📝 Get the notes for free here: https://courses.physicswithelliot.com... ✉️ Sign up for my newsletter for additional physics lessons: https://courses.physicswithelliot.com... 📺 Part I: Foundations of quantum mechanics    • But why wavefunctions? A practical ap...   📺 Part II: Discovering the path integral and the classical limit    • How Feynman did quantum mechanics (an...   🅿 Become a patron to help make videos like these possible:   / physicswithelliot   👨‍🏫 Enroll in my course on Lagrangian mechanics! https://bit.ly/lagrangian-fundamentals 🙋‍♀️ "What software did you use to make this video?" and other FAQs: https://www.physicswithelliot.com/faq 📖 Video summary: 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. 🏷️ Chapters: 0:00 Introduction 4:12 Review of quantum mechanics 9:32 Defining the path integral 16:55 Example: the free particle 22:07 Uncertainty principle 24:15 Back to the wavefunction 26:19 Next steps If you find the content I’m creating valuable and would like to help make it possible for me to continue sharing more, please consider supporting me! You can make a recurring contribution at   / physicswithelliot  , or make a one time contribution at https://www.physicswithelliot.com/sup.... Thank you so much! About me: I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at https://www.physicswithelliot.com.