Why Relativity Breaks the Schrodinger Equation

In this video, we look at why the Schrodinger equation is incompatible with special relativity, specifically through the lens of Schrodinger plane waves, and the energy vs. velocity curves for relativistic and classical physics.

Stay tuned for the next videos, in which we will derive relativistic wave equations, explore the four-potential and gauge symmetry, and eventually will return to hydrogen with a relativistic treatment of the electron! :)

For further reading, please check out Introduction to Elementary Particles, by David Griffiths. That book provides a ton of insightful context around the ideas in this quantum physics playlist.

Chapters:

0:00 Intro
0:50 Schrödinger Free Particle
2:00 2nd Order in Space, 1st in Time
2:52 Schrödinger Plane Waves
5:03 de Broglie Relations
6:55 Relativistic vs. Classical E(v) Curves
13:00 Ultra-relativistic LEP Electron
14:34 Returning to the Plane Waves
15:44 Concluding Remarks

#physics #quantum #math

[RichBehiel]

Hey everyone, thanks for checking out this video! :) Just wanted to pin a couple of minor corrections here, based on your feedback:

1) I should have put “keV” instead of “KeV”. It’s like how kilogram is kg, not Kg.

2) I should have clarified that typically (Laplacian) ~ (d/dt) is called the heat equation or diffusion equation, whereas the term “wave equation” typically connotes (Laplacian) ~ (d2/dt2). *However*, that’s because we often use real-valued functions; when working with complex-valued functions, (Laplacian) ~ (d/dt) does indeed allow for wave solutions, because of the phase degree of freedom in the complex plane. The plane waves shown in this video are examples of that. But instead of just saying that S.E. for a free particle is a wave equation, I should have talked briefly about how the first time derivative requires that psi be complex, at which point this thing that looks like diffusion can actually get wavy. I hope that explanation clears things up.

Please let me know if you have any more corrections for this video. I’m trying to always get better over time! :)

[jimbobjr]

You are the 3blue1brown of physics. Some of the highest quality videos on youtube. Thank you sir

[arturchakhvadze]

Somehow you are hitting this magical sweet spot where every time you explain some profound result I feel like “yeah, this makes perfect sense”.

[wlfellinUT]

First rate pedagogy - always love learning from experts who are totally at ease with their topic.

[rq]

I just want to say that I appreciate this so much. This is the level I'm at, and its hard to find content that doesnt hold back from the whole truth, while still giving a good intuition and not falling back to the math alone pretending that understanding the math is the same as understanding the thing itself.

[RagaarAshnod]

0:08 intro
0:50 free particle
2:00 2nd order space
2:52 plane waves
5:03 de broglie
6:55 curves
13:00 lep electron
14:34 return to plane waves
15:44 conclusion

[LeoMarchyok-odby]

Studied advanced physics in high school and just did vector calc in university. I’m so happy to finally understand this stuff!

[jakublizon]

This is exactly what I've been looking for. I need to see the math. General concepts don't satisfy my curiosity anymore. Well, they do but in some areas I really crave a deeper understanding and linear algebra helps with that.

[jensphiliphohmann]

I'd love to actually see a video about DIRAC's trick to form a 1st order equation and how it automatically predicts both spin and antiparticles.

[nicholasspicer]

im always so excited to see your posts. you by far have the most informative content on youtube about quantum mechanics and WHY things are the way they appear. thank you for doing what you do, and once again illuminating a topic that's well known but whos facets are rarely seen.

[onnilattu]

I love your content since its not just your typical edutainment physics shit with diluted details and simplified explanations. Instead you present actual physics with real equations

[Robinson]

"Saying that number makes me sound like a stubborn German" - made my day

[greenmario]

As someone with a chemistry background I mostly knew about relativity's effects on electron clouds as the reason heavy element chemistry stops making sense and just sorta does whatever it wants.

[DrJens-pnqk]

The Schrödinger equation is actually no wave equation but a diffusion equation (Laplace operator proportional to 1st(!) time derivative).

[guylan]

Great video!
U obviously a PRO!
Please share in the description the relevant academic bibliography for further reading.
ThX!

[uva]

this channel is a godsend!! coming from a pure maths background your videos are a perfect transition into physics

[wafikiri_]

Much that most in this video is right on-the-spot, there is a tiny detail that is not. In the metric system, all the dividing prefixes use a lowercase letter: d for deci-, c for centi-, m for milli-, etc. And, all the multiplying prefixes, an uppercase letter: D for deca-, H for hecto-, ... and K for kilo-. But it is not KeV, Km, or Kg that are written on the graphics in the video, but keV, km, and kg instead. A little detail but it should be corrected.
Anyway, thanks for the video. Very educational and interesting.

[WaluigiisthekingASmith]

You're such a tease :)

All of your videos are so good but they always leave me wanting all the things you hint at. Maybe one day you'll get to spin statistics and I'll finally understand why QM forbids particles that arent spin n or n+1/2

[heniohenrykowski]

The stubborn-German joke (13:50) made my day! :-)))

[Mathymagical]

I was sitting here wondering why there was no third video in the series. It was just uploaded! Good work! Subscribed.