Topics (206k) Articles (211k) Users (303) Discussions (237) Comments (383) Files (716) New article
We get the time-independent Schrödinger equation by substituting this into Equation "time-independent Schrödinger equation for a one dimensional particle":
Now, there are two ways to go about this.
The first is the stupid "here's a guess" + "hey this family of solutions forms a complete basis"! This is exactly how we solved the problem at Section "Solving partial differential equations with the Fourier series", except that now the complete basis are the Hermite functions.
The second is the much celebrated ladder operator method.
Examples:
- flash memory uses quantum tunneling as the basis for setting and resetting bits
- alpha decay is understood as a quantum tunneling effect in the nucleus
Is the only atom that has a closed form solution, which allows for very good predictions, and gives awesome intuition about the orbitals in general.
It is arguably the most important solution of the Schrodinger equation.
In particular, it predicts:
- the major spectral line of the hydrogen atom by taking the difference between energy levels
The explicit solution can be written in terms of spherical harmonics.
Solutions for the Schrodinger equation with multiple particles by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Bibliography:
- Quantum Mechanics for Engineers by Leon van Dommelen (2011) "5. Multiple-Particle Systems"
Discrete quantum system model that can model both spin in the Stern-Gerlach experiment or photon polarization in polarizer.
Predicts fine structure.
Bibliography:
How To Solve The Dirac Equation For The Hydrogen Atom | Relativistic Quantum Mechanics by Dietterich Labs (2018)
Source. You can't just shred individual sSD files because SSD writes only at large granularities, so hardware/drivers have to copy stuff around all the time to compact it. This means that leftover copies are left around everywhere.
What you can do however is to erase the entire thing with vendor support, which most hardware has support for. On hardware encrypted disks, you can even just erase the keys:
TODO does shredding the
www.quora.com/Why-do-successful-geeky-white-men-have-Asian-wives-This-seems-to-be-the-norm-in-Silicon-Valley suggests it is just an statistical inevitability.
Ciro Santilli believes that there is a positive correlation between being a software engineer and liking Buddhist-like things.
Maybe it is linked to minimalism and DRY, which software engineers value so greatly.
Even Ciro had to try an unoriginal Buddhist joke intro in one of this Stack Overflow answers.
Ciro also feels that his "minimal reproducible example" scientific language/concept learning method obsession of breaking things into tiny sub-problems has a strong link with Koans.
Some notable Buddhism/programmer examples:
- www.catb.org/~esr/writings/unix-koans/ "The Unix Koans of Master Foo - Rootless Root (无根的根)" by the legendary Eric Steven Raymond is notable
- thecodelesscode.com/ "The Codeless Code" by anonymous Qi.
- canonical.org/~kragen/tao-of-programming.html
- wiki.c2.com/?MysticalProgrammingKoans
- rubykoans.com/ even evil programming languages adopt them!
- The Zen of Python
Another thing that points the correlation out is the existence of wattsalan.github.io/ on a
github.io about Alan Watts.Institutional video about the 1974 single electron experiment by Merli, Missiroli, Pozzi from the University of Bologna.
Then actually show the result live on a television screen, where you see the interference patterns only at higher electron currents, and then on photographic film.
This was elected "the most beautiful experiment" by readers of Physics World in 2002.
Ciro Santilli's wife, who was frustrated with academia at some point, admires the fact that Simons managed to make infinite money, and then invested back in actual science, e.g. through the Simons Foundation.
Jim Simons in 2007
. Claims provably fair. satoshidice.com/fair clarifies what that means: they prove fairness by releasing a hash of the seed before the bets, and the actual seed after the bets.
Scientific Autobiography by Max Planck translated by Frank Gaynor (1949) by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Published as Scientific Autobiography and Other Papers by Max Planck translated by Frank Gaynor (1949) which also contained other papers.
This section refers just to the translation of Scientific autobiography by Max Planck (1948).
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