Predicts fine structure.
Bibliography:
Dirac equation for the electron and hydrogen Hamiltonian by Barton Zwiebach (2019)
Source. Uses perturbation theory to get to the relativistic corrections of fine structure! Part of MIT 8.06 Quantum Physics III, Spring 2018 by Barton ZwiebachHow To Solve The Dirac Equation For The Hydrogen Atom | Relativistic Quantum Mechanics by Dietterich Labs (2018)
Source. Spin is one of the defining properties of elementary particles, i.e. number that describes how an elementary particle behaves, much like electric charge and mass.
The approach shown in this section: Section "Spin comes naturally when adding relativity to quantum mechanics" shows what the spin number actually means in general. As shown there, the spin number it is a direct consequence of having the laws of nature be Lorentz invariant. Different spin numbers are just different ways in which this can be achieved as per different Representation of the Lorentz group.
Video 1. "Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)" explains nicely how:
- incorporated into the Dirac equation as a natural consequence of special relativity corrections, but not naturally present in the Schrödinger equation, see also: the Dirac equation predicts spin
- photon spin can be either linear or circular
- the linear one can be made from a superposition of circular ones
- straight antennas produce linearly polarized photos, and Helical antennas circularly polarized ones
- a jump between 2s and 2p in an atom changes angular momentum. Therefore, the photon must carry angular momentum as well as energy.
- cannot be classically explained, because even for a very large estimate of the electron size, its surface would have to spin faster than light to achieve that magnetic momentum with the known electron charge
- as shown at Video "Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)", observers in different frames of reference see different spin states
Quantum Spin - Visualizing the physics and mathematics by Physics Videos by Eugene Khutoryansky (2016)
Source. - Stern-Gerlach experiment
- fine structure split in energy levels
- anomalous Zeeman effect
- of a more statistical nature, but therefore also macroscopic and more dramatically observable:
- ferromagnetism
- Bose-Einstein statistics vs Fermi-Dirac statistics. A notable example is the difference in superfluid transition temperature between superfluid helium-3 and superfluid helium-4.
Originally done with (neutral) silver atoms in 1921, but even clearer theoretically was the hydrogen reproduction in 1927 by T. E. Phipps and J. B. Taylor.
The hydrogen experiment was apparently harder to do and the result is less visible, TODO why: physics.stackexchange.com/questions/33021/why-silver-atoms-were-used-in-stern-gerlach-experiment
The Stern-Gerlach Experiment by Educational Services, Inc (1967)
Source. Featuring MIT Professor Jerrold R. Zacharias. Amazing experimental setup demonstration, he takes apart much of the experiment to show what's going on.Introduction to Spintronics by Aurélien Manchon (2020)
Source. The Spin on Electronics by Stuart Parkin
. Source. 2013.Basic component in spintronics, used in both giant magnetoresistance
What is spintronics and how is it useful? by SciToons (2019)
Source. Gives a good 1 minute explanation of tunnel magnetoresistance.Introduction to Spintronics by Aurélien Manchon (2020) giant magnetoresistance section
. Source. Describes how giant magnetoresistance was used in magnetoresistive disk heads in the 90's providing a huge improvement in disk storage density over the pre-existing inductive sensors
More comments at: Video "Introduction to Spintronics by Aurélien Manchon (2020)".
Introduction to Spintronics by Aurélien Manchon (2020) spin-transfer torque section
. Source. Describes how how spin-transfer torque was used in magnetoresistive RAM
More comments at: Video "Introduction to Spintronics by Aurélien Manchon (2020)".
Leads to the Dirac equation.
Leads to the Proca equation.
Theorized for the graviton.
More interestingly, how is that implied by the Stern-Gerlach experiment?
physics.stackexchange.com/questions/266359/when-we-say-electron-spin-is-1-2-what-exactly-does-it-mean-1-2-of-what/266371#266371 suggests that half could either mean:
- at limit of large
lfor the Schrödinger equation solution for the hydrogen atom the difference between each angular momentum is twice that of the eletron's spin. Not very satisfactory. - it comes directly out of the Dirac equation. This is satisfactory. :-)
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact