This is the order in which a binary search tree should be traversed for ordered output, i.e.:
- everything to the left is smaller than parent
- everything to the right is larger than parent
This ordering makes sense for binary trees and not k-ary trees in general because if there are more than two nodes it is not clear what the top node should go in the middle of.
This is unlike pre-order depth-first search and post-order depth-first search which generalize obviously to general trees.
This is the easiest one to do iteratively:
- pop and visit
- push right to stack
- push left to stack
The summary from www.geeksforgeeks.org/tree-traversals-inorder-preorder-and-postorder/ is a winner:
1
/ \
2 3
/ \
4 5- inorder DFS: 4 2 5 1 3
- preorder DFS: 1 2 4 5 3
- postorder DFS: 4 5 2 3 1
- breadth-first search: 1 2 3 4 5
In principle one could talk about tree traversal of unordered trees as a number of possible traversals without a fixed order. But we won't consider that under this section, only deterministic ordered tree traversals.
@cirosantilli/_file/graphviz/graphviz/quotes.dot by 
Ciro Santilli 35 Updated 2025-04-16 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-16 +Created 1970-01-01 @cirosantilli/_file/graphviz/graphviz/quotes-escape.dot by Ciro Santilli 35 Updated 2025-04-16 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-16 +Created 1970-01-01 Quantization as an Eigenvalue Problem by Ciro Santilli 35 Updated 2025-04-16 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-16 +Created 1970-01-01This paper appears to calculate the Schrödinger equation solution for the hydrogen atom.
TODO is this the original paper on the Schrödinger equation?
Published on Annalen der Physik in 1926.
Open access in German at: onlinelibrary.wiley.com/doi/10.1002/andp.19263840404 which gives volume 384, Issue 4, Pages 361-376. Kudos to Wiley for that. E.g. Nature did not have similar policies as of 2023.
This paper may have fallen into the public domain in the US in 2022! On the Internet Archive we can see scans of the journal that contains it at: ia903403.us.archive.org/29/items/sim_annalen-der-physik_1926_79_contents/sim_annalen-der-physik_1926_79_contents.pdf. Ciro Santilli extracted just the paper to: commons.wikimedia.org/w/index.php?title=File%3AQuantisierung_als_Eigenwertproblem.pdf. It is not as well processed as the Wiley one, but it is of 100% guaranteed clean public domain provenance! TODO: hmmm, it may be public domain in the USA but not Germany, where 70 years after author deaths rules, and Schrodinger died in 1961, so it may be up to 2031 in that country... messy stuff. There's also the question of wether copyright is was tranferred to AdP at publication or not.
An early English translation present at Collected Papers On Wave Mechanics by Deans (1928).
Contains formulas such as the Schrödinger equation solution for the hydrogen atom (1''):where:
In order for there to be numerical agreement, must have the value
, are the charge and mass of the electron
Average number of steps until reaching a state of a Markov chain by Ciro Santilli 35 Updated 2025-04-16 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-16 +Created 1970-01-01TODO how to calculate
Pinned article: ourbigbook/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!
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/derivative - 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 4. Visual Studio Code extension tree navigation.
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.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - Internal cross file references done right:
- Infinitely deep tables of contents:
Figure 6. Dynamic article tree with infinitely deep table of contents.Live URL: ourbigbook.com/cirosantilli/chordateDescendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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