These are the key mathematical ideas to understand!!
There are actually a few formulations out there. By far the dominant one as of 2020 has been the Schrödinger picture, which contrasts notably with the Heisenberg picture.
Another well known one is the de Broglie-Bohm theory, which is deterministic, but non-local.
The first quantum mechanics theories developed.
Their most popular formulation has been the Schrödinger equation.
Quarks, Gluon flux tubes, Strong Nuclear Force, & Quantum Chromodynamics by Physics Videos by Eugene Khutoryansky (2018)
Source. Some decent visualizations of how the field lines don't expand out like they do in electromagnetism, suggesting color confinement.PHYS 485 Lecture 6: Feynman Diagrams by Roger Moore (2016)
Source. Despite the title, this is mostly about QCD. Quantum field theory lecture by Tobias Osborne (2017) Lecture 4 by
Ciro Santilli 37 Updated 2025-07-16
- quantization. Uses a more or less standard way to guess the quantized system from the classical one using Hamiltonian mechanics.
- youtu.be/fnMcaq6QqTY?t=1179 remembers how to solve the non-field quantum harmonic oscillator
- youtu.be/fnMcaq6QqTY?t=2008 puts hats on everything to make the field version of things. With the Klein-Gordon equation Hamiltonian, everything is analogous to the harmonic oscilator
Problem Book in Quantum Field Theory by Voja Radovanovic (2008) by
Ciro Santilli 37 Updated 2025-07-16
Too many fun skit videos for Ciro Santilli's taste, but does have some serious derivations in quantum electrodynamics.
Derived from classical first principles, matches Planck's law for low frequencies, but diverges at higher frequencies.
The type of laser described at: Video "How Lasers Work by Scientized (2017)", notably youtu.be/_JOchLyNO_w?t=581. Mentioned at: youtu.be/_JOchLyNO_w?t=759 That point also mentions that 4-level lasers also exist and are more efficient. TODO dominance? Alternatives?
Bibliography:
English translation of papers that include the original Quantization as an Eigenvalue Problem by Schrödinger (1926).
Published on Nature at www.nature.com/articles/122990a0 and therefore still paywalled there as of 2023, it's ridiculous.
In 2024 it will fall into the public domain in the US.
How To Get Tenure at a Major Research University by Sean Carroll (2011) by
Ciro Santilli 37 Updated 2025-07-16
Power, Sex, Suicide by Nick Lane (2006) part 5 "Murder or suicide" mentions that the key events that leads to apoptosis is when certain proteins normally present in the inner mitochondrial membrane spill out, and that this often happens when free radicals are produced in excess: the cell is really not doing well in those cases. This point suggests that the initial mitochondrial endosymbiosis happened due to a parasite that lived inside another cell. It mentions that even today we see parasites kill the host cell when they feel that the cell does not have many nutrients. This frees the parasites to then infect other cells.
Follows the "certified teacher only" approach which is in Ciro Santilli's opinion a fatal flaw of most elearning systems out there, OurBigBook.com won't suffer from that!
All notes appear to have been extracted from existing notes, as noted on the bottom of each page.
Appears to have mixed licenses. E.g.:
- phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/06%3A_Photons_and_Matter_Waves/6.06%3A_De_Broglies_Matter_Waves is CC BY
- but we had seen another one that was CC BY-NC-SA
- phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_9HE_-_Modern_Physics/06%3A_Emission_and_Absorption_of_Photons/6.1%3A_Transitions_Between_Stationary_States CC BY-SA
- chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12) uses the custom "CK-12 license" which seems a bit like CC BY-NC-SA
- some don't even have a free license, e.g.: phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_(Fowler)/00%3A_Front_Matter/04%3A_Licensing
TODO how does it work exactly? Do they ask for permission from authors in every case, including when the content has open license? Or when it has open license, do they just do it? In some cases, the notes have no license, so they must have asked.
TODO what is the source code that authors write? LaTeX or something else? LaTeX feels extremely likely given that it is what most original materials were already written in.
They are attempting a "model up this entire university" thing: phys.libretexts.org/Courses which is good. E.g. they have a bunch of "quantum mechanics ones under: phys.libretexts.org/Bookshelves/Quantum_Mechanics
Appears to be UC Davies-based mostly.
They claim to use this closed source backend: www.nice.com/resources/cxone-expert-knowledge-management? Seriously? For a publicly funded project with low-tech requirements?? It is mind blowing.
Some issues:
- the internal cross references are somewhat broken as of 2022.
- their URLs are HUGE! All components of every ancestor are in it. E.g. check this out: phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introductory_Quantum_Mechanics_(Fitzpatrick)/12%3A_Time-Dependent_Perturbation_Theory/12.13%3A_Forbidden_Transitions Insane.
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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . 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. - 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