Relativistic Quantum Waves (Klein-Gordon Equation)

In this video, we'll unify special relativity and quantum mechanics, to derive the beautiful Klein-Gordon equation! Then we'll explore some of its properties, to see what it can (and can't) tell us about the nature of things. This is part of a video series that's building toward an exploration of the Dirac equation, and then a triumphant return to the hydrogen atom.

Thanks for checking out this video, and if you are so inclined, please consider joining my Patreon, for full access to the slides from these videos, and additional notes and links to supplemental materials. I'll also be on there to answer any questions you might have about physics, math, and life, and your input will help guide the future direction of this channel. All support is greatly appreciated.

Chapters:

0:00 Intro
1:40 Deriving the KG Equation
7:24 Four-Momentum Eigenstates
12:38 Superposition
14:36 KG vs Schrödinger
16:48 Group Velocity & c Speed Limit
23:16 Fourier Transforms & Antimatter
31:01 The 2nd-Order-in-Time Problem
33:15 Probability Density & Current
39:55 The Mystery of Spin
42:27 Concluding Remarks by Paul Dirac

#physics #math #quantum #relativity

[TheoriesofEverything]

Resplendent. This outpaces any single chapter in a book and any single lecture I've seen on KG.

[enotdetcelfer]

Absolute clarity, wow. I'll never look at the mass shell, position and momentum, and the speed of light the same again. Between this and having watched eigenchris' spinor videos on a loop, all my childhood discomfort with traditional metaphors completely disappeared and I think I finally understand. I can't thank you enough, it all finally clicked. And they knew this so back in the 20s huh?! You turned the formulas into sheet music and those visuals were so intuitive. Everything as degrees of freedom in this pure math. I gotta watch this like 10 more times and let it really sink in. Thank you so much.

[ProfessorBeautiful]

As a physics fanboy with moderate math, I greatly appreciate this video, with many gems of insight tying things together I knew only from snippets. And... to hear DIRAC speak! What a treat--the gentlest possible use of the word 'intolerable'!

[KipIngram]

I was astounded when I learned that in his later years Dirac regarded his life's work as a failure. My God - if Dirac was a failure, then we have no successes. He's literally at the top of the heap as far as I'm concerned.

[thekey]

Thank you for giving a clear concise explanation of these equations that doesn’t require 2 years of obnoxious jargon training.

[trucid]

14:39 That transition was so awesome I had to watch it multiple times.

[diana-pestana]

Really liked how you easily presented the topic, adding historical and philosophical context. Great video!

[gianlaager]

I just started college and I did as my "high school thesis" (not a really good translation) a approximation of the Schroedinger equation because I wanted to see what these waves looked like. Thank you for giving us those animations along side a quite in depth explanation of the math. Keep it going!

[michaelblankenau]

Even though I can't understand any of this ( and that's 100% on me ) I still give you a like because intuitively I know you have done a great job .

[trucid]

Just wanted to say that your video is a masterpiece. I'm not just saying that. Usually when I see equations in physics videos my eyes just glaze over and I stop paying attention. You made it so simple to understand that apart from the latter part where you started talking about eigenvectors I followed all of it.

[purplenanite]

It looks amazing! I loved the closing remarks by Dirac.

[ohno]

Losing my mind at "a square is like if a triangle had four sides"

[alverpo]

Cant wait to see the Dirac equation video. I totally trust you to finally get me to understand the spinors.

[calummoncrieff]

Love the Superposition section, these videos are beautifully put together. Down to earth explanations on complex topics. 👍👍

[LuisAldamiz]

I must admit I only grasp the maths somewhat but the explanation and the graphics are awesome.

[vbdatabase]

I don't have much, bu your videos are priceless please keep making them.

[Phantores]

One of my favourite channels uploaded another amazing mathy video again

[Danzerocalories]

I'm considering going back to school for physics and this playlist is awesome! Thank you for such a clear explanation and visual presentation!

[gavinwince]

When I saw you start this off with + --- I knew this was going to be good!

[aieousavren]

Absolutely incredible work! I don't mean to simply blindly add more praise to the pile of already glowing comments, but I genuinely really appreciate this series and your hard work that you clearly put into it. I enjoy the style of your thinking and your presentation, the visuals are of course gorgeous, and the mathematical details really fill everything out.

I've learned a ton from your approach to thinking about quantum mechanics, and I continue to watch eagerly and wait patiently for this great work to continue.

Every time you upload, it is a joy. Thank you so much! ❤