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Currently Playing: Spinors for Beginners 23: Klein-Gordon Equation (derivation + solutions)

Full spinors playlist: https://www.youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBs Leave me a tip: https://ko-fi.com/eigenchris Powerpoint slide files + Exercise answers: https://github.com/eigenchris/MathNotes/tree/master/SpinorsForBeginners Wikipedia article on phase velocity and group velocity: https://en.wikipedia.org/wiki/Group_velocity 0:00 - Introduction 1:42 - Klein-Gordon Lagrangian 7:43 - Klein Gordon Solutions 13:58 - Phase velocity and Group velocity 20:05 - Dispersion Relation 21:20 - Complex KG Field, Anti-matter, U(1) 26:54 - Quantum Fields 27:52 - Summary