Show up in the solution of the quantum harmonic oscillator after separation of variables leading into the time-independent Schrödinger equation, much like solving partial differential equations with the Fourier series.
I.e.: they are both:
- solutions to the time-independent Schrödinger equation for the quantum harmonic oscillator
- a complete basis of that space
Historical correspondence between Latin and Greek by 
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01 History of condensed matter physics by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01 PCR verification with gel electrophoresis by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01For this reason, it is wise to verify that certain steps are correct whenever possible.
Gel electrophoresis separates molecules by their charge-to-mass ratio. It is one of those ultra common lab procedures!
Since we know that we amplified the 16S regions which we know the rough size of (there might be a bit of variability across species, but not that much), we were expecting to see a big band at that size.
And that is exactly what we saw!
First we had to prepare the gel, put the gel comb, and pipette the samples into wells present in the gel:
To see the DNA, we added ethidium bromide to the samples, which is a substance that that both binds to DNA and is fluorescent.
Because it interacts heavily with DNA, ethidium bromide is a mutagen, and the biology people sure did treat the dedicated electrophoresis bench area with respect! Figure 4. "Gel electrophoresis dedicated bench area to prevent ethidium bromide contamination.".
Gel electrophoresis dedicated waste bin for centrifuge tubes and pipette tips contaminated with ethidium bromide.
Source. The UV transilluminator we used to shoot UV light into the gel was the Fisher Scientific UVP LM-26E Benchtop 2UV Transilluminator. The fluorescent substance then emitted a light we can see.
As barely seen at Figure 8. "Fischer Scientific UVP LM-26E Benchtop 2UV Transilluminator illuminated gel." due to bad photo quality due to lack of light, there is one strong green line, which compared to the ladder matches our expected 16S length. What we saw it with the naked eyes was very clear however.
Horrible Horrendous Terrible Tremendous by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01They might have shut down, but they still have the cutest name! And they've made some cute inscriptions too, see: HHTT
How can a chemical substance be unstable but not flammable? by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01 How many logical qubits are needed to run Shor's algorithm? by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01How to decide if an ORM is decent? Just try to replicate every SQL query from nodejs/sequelize/raw/many_to_many.js on PostgreSQL and SQLite.
There is only a very finite number of possible reasonable queries on a two table many to many relationship with a join table. A decent ORM has to be able to do them all.
If it can do all those queries, then the ORM can actually do a good subset of SQL and is decent. If not, it can't, and this will make you suffer. E.g. Sequelize v5 is such an ORM that makes you suffer.
The next thing to check are transactions.
Basically, all of those come up if you try to implement a blog hello world world such as gothinkster/realworld correctly, i.e. without unnecessary inefficiencies due to your ORM on top of underlying SQL, and dealing with concurrency.
How to diagnose a genius by Wilhelm Ostwald (1909) by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01From the abstract:Ciro Santilli couldn't agree more... notably students must have a flexible choice of what to learn.
Much money, his student went on to say, is spent by various Governments in attempting to discover those people whose thorough education may be expected to bring in a return of value to the State, and the question how best to discover latent genius is an eminently practical one. After cogitation, Prof. Ostwald came to the conclusion that it is those students who cannot be kept on the rails - that is, who are not contented with methodical teaching - who have within them the seeds of genius
How To Get Tenure at a Major Research University by Sean Carroll (2011) by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01 How to run a MicroPython script from a file on the Raspberry Pi Pico W from the command line? by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01The first/only way Ciro could find was with ampy: stackoverflow.com/questions/74150782/how-to-run-a-micropython-host-script-file-on-the-raspbery-pi-pico-from-the-host/74150783#74150783 That just worked and it worked perfectly!
python3 -m pip install --user adafruit-ampy
ampy --port /dev/ttyACM0 run blink.pyscholarworks.sjsu.edu/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=5051&context=etd_theses proves that the Mathieu group is simple in just 200 pages. Nice.
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!
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