Lagrange's identity is a mathematical formula that relates the sums of squares of two sets of variables. It is often stated in the context of inner product spaces or in terms of quadratic forms.
The book unfortunately does not cover the history of quantum mechanics very, the author specifically says that this will not be covered, the focus is more on particles/forces. But there are still some mentions.
The Nexon Computer Museum is a museum located in Seongnam, South Korea, dedicated to the history and culture of computers and gaming. Opened in 2018, it is a part of Nexon, a well-known video game company, and aims to preserve and showcase the evolution of computer technology and gaming from the 20th century to the present day.
The time-independent Schrödinger equation is a variant of the Schrödinger equation defined as:
Equation 1.
Time-independent Schrodinger equation
. So we see that for any Schrödinger equation, which is fully defined by the Hamiltonian , there is a corresponding time-independent Schrödinger equation, which is also uniquely defined by the same Hamiltonian.
The cool thing about the Time-independent Schrödinger equation is that we can always reduce solving the full Schrödinger equation to solving this slightly simpler time-independent version, as described at: Section "Solving the Schrodinger equation with the time-independent Schrödinger equation".
Because this method is fully general, and it simplifies the initial time-dependent problem to a time independent one, it is the approach that we will always take when solving the Schrodinger equation, see e.g. quantum harmonic oscillator.
2011 PHYS 485 lecture videos by Roger Moore from the University of Alberta by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16Too many fun skit videos for Ciro Santilli's taste, but does have some serious derivations in quantum electrodynamics.
Covers some specific hardcore subjects, notably quantum electrodynamics, in full mathematical detail, e.g.: "Quantum Field Theory Lecture Series" playlist: www.youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
As of 2020 Dietterich was a condensed matter PhD candidate or post-doc at the University of Minnesota Twin Cities, and he lives in Minnesota, sources:
Unfortunately the channel is too obsessed with mathematical detail (which it does amazingly), and does not give enough examples/application/intuition, which is what would be useful to most people, thus falling too much on the hardcore side of the missing link between basic and advanced.
This channel does have on merit however: compared to other university courses, it is much more direct, which might mean that you get to something interesting before you got bored to death, Section "You can learn more from older students than from faculty" comes to mind.
Videos generally involves short talks + a detailed read-through of a pre-prepared PDF. Dietterich has refused however giving the PDF or LaTeX source as of 2020 on comments unfortunately... what a wasted opportunity for society. TODO find the comment. Sam, if you ever Google yourself to this page, let's make a collab on OurBigBook.com and fucking change education forever man.
The Ultimate Goal Of My YouTube Channel by Dietterich Labs (2020)
Source. In this video Dietterich gives his ideal for the channel. Notably, he describes how the few experimental videos he has managed to make were done in a opportunistic way from experiments that were happening around him. This resonated with Ciro Santilli's ideas from videos of all key physics experiments.Sam Dietterich interview by Dietterich Labs (2022)
Source. TODO find patience to watch and summarize key points.The Sting Of Soft Corruption: My College Experience by Dietterich Labs
. Source. Academia is broken video.Those guys are really good, Ciro Santilli especially enjoyed their quantum mechanics playlist: www.youtube.com/playlist?list=PL193BC0532FE7B02C
The quantum electrodynamics one was a bit too slow paced for Ciro unfortunately, too much groundwork and too little results.
These videos can give some geometric insight and do have their value.
But they are sometimes too slow, there are never any mention of experiments, just "the truth".
Eugene's background: www.quora.com/Who-is-Eugene-Khutoryansky/answer/Ciro-Santilli
Publishes through the Fermilab YouTube channel under the playlist "Fermilab - Videos by Don Lincoln"
Some insights, but too much on the popular science side of things.
- why the square: physics.stackexchange.com/questions/535/why-does-kinetic-energy-increase-quadratically-not-linearly-with-speed on Physics Stack Exchange. Ron Maimon's answer is great, as it relies only on the following staring points:He also offers a symmetry argument considering the case of potential energy.
- why the half: physics.stackexchange.com/questions/27847/why-is-there-a-frac-1-2-in-frac-1-2-mv2 on Physics Stack Exchange
- physics.stackexchange.com/questions/26797/why-does-work-equal-force-times-distance
- www.quora.com/Why-do-we-define-work-as-force-times-distance
- physics.stackexchange.com/questions/428525/why-does-work-depend-on-distance
- physics.stackexchange.com/questions/79523/why-does-the-amount-of-energy-transferred-depend-on-distance-rather-than-time
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