Appears directly on Schrödinger equation! And in particular in the time-independent Schrödinger equation.
There is also a time-energy uncertainty principle, because those two operators are also complementary.
Then you have to understand what each one of those does to the each atomic orbital:
- total angular momentum: determined by the azimuthal quantum number
- angular momentum in one direction ( by convention): determined by the magnetic quantum number
There is an uncertainty principle between the x, y and z angular momentums, we can only measure one of them with certainty at a time. Video 1. "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)" justifies this intuitively by mentioning that this is analogous to precession: if you try to measure electrons e.g. with the Zeeman effect the precess on the other directions which you end up modifing.
TODO is there any good intuitive argument or proof of conservation of energy, momentum, angular momentum?
Conservation of the square amplitude in the Schrodinger equation by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16It can be derived directly from the Schrödinger equation.
Bibliography:
- That proof also mentions that if the potential
Vis not real, then there is no conservation of probability! Therefore the potential must be real valued!
Contains the full state of the quantum system.
This is in contrast to classical mechanics where e.g. the state of mechanical system is given by two real functions: position and speed.
The wave equation in position representation on the other hand encodes speed in "how fast does the complex phase spin around", and direction in "does it spin clockwise or counterclockwise", as described well at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)". Then once you understand that, it is more compact to just view those graphs with the phase color coded as in Video "Simulation of the time-dependent Schrodinger equation (JavaScript Animation) by Coding Physics (2019)".
Diffraction of Cathode Rays by a Thin Film by Thomson and Reid (1927) by Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16
Quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925) by Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16This Heisenberg's breakthrough paper on matrix mechanics which later led to the Schrödinger equation, see also: history of quantum mechanics.
Published on the Zeitschrift für Physik volume 33 page pages 879-893, link.springer.com/article/10.1007%2FBF01328377
Modern overview: www.mat.unimi.it/users/galgani/arch/heisenberg25amer_j_phys.pdf
Deterministic, but non-local.
And analogously for matter, appears in the de Broglie relations relating momentum and frequency. Also appears in the Schrödinger equation, basically as a consequence/cause of the de Broglie relations most likely.
Intuitively, the Planck constant determines at what length scale do quantum effects start to show up for a given energy scale. It is because the Plank constant is very small that we don't perceive quantum effects on everyday energy/length/time scales. On the , quantum mechanics disappears entirely.
A very direct way of thinking about it is to think about what would happen in a double-slit experiment. TODO think more clearly what happens there.
Defined exactly in the 2019 redefinition of the SI base units to:
Appears in the Schrödinger equation.
The first really good quantum mechanics theory made compatible with special relativity was the Dirac equation.
And then came quantum electrodynamics to improve it: Dirac equation vs quantum electrodynamics.
TODO: does it use full blown QED, or just something intermediate?
www.youtube.com/watch?v=NtnsHtYYKf0 "Mercury and Relativity - Periodic Table of Videos" by Periodic Videos (2013). Doesn't give the key juicy details/intuition. Also mentioned on Wikipedia: en.wikipedia.org/wiki/Relativistic_quantum_chemistry#Mercury
Explaining this was was one of the key initial achievements of the Dirac equation.
Yes, but this is not predicted by the Schrödinger equation, you need to go to the Dirac equation.
See also:
- physics.stackexchange.com/questions/233330/why-do-electrons-jump-between-orbitals
- physics.stackexchange.com/questions/117417/quantum-mechanics-scattering-theory/522220#522220
- physics.stackexchange.com/questions/430268/stimulated-emission-how-can-giving-energy-to-electrons-make-them-decay-to-a-low/430288
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
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- 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. 
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