Quantizing the Klein-Gordon Field as Harmonic Oscillators - FULLY EXPLAINED!

In this video I will explain how to quantize the Klein-Gordon field using harmonic oscillators as an analogy. I will go through every step to ensure that you understand it all!

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My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00:00 Introducing the objective of the video
00:01:15 Reminder of Lagrangian & Hamiltonian Mechanics for single particle
00:03:20 Going from single particle to a field
00:07:20 Finding the Hamiltonian for the Classical Klein-Gordon Field
00:10:05 Quantizing the Klein-Gordon Field
00:13:30 Understanding why we can think of a field as Harmonic Oscillators
00:18:10 Reminder of Harmonic Oscillator & Explaining what comes next
00:32:20 Doing the Same Procedure but with QFT (Field Decomposition)
00:39:00 Writing the Field in terms of ladder operators
00:46:30 Introducing a new normalization (due to convention)
00:50:00 Finding the conjugate momentum of the field (pi)
00:51:40 Changing notation to match Peskin Schroeder
00:57:40 Checking the commutator of phi and pi (field and momentum)
01:06:28 Write the Hamiltonian in terms of ladder operators
01:24:00 Please consider supporting my patreon!