Quantum tunnelling by Ciro Santilli 40 Updated 2025-07-16
Examples:
Position operator by Ciro Santilli 40 Updated 2025-07-16
This operator case is surprisingly not necessarily mathematically trivial to describe formally because you often end up getting into the Dirac delta functions/continuous spectrum: as mentioned at: mathematical formulation of quantum mechanics
Basically the operators are just analogous to the classical ones e.g. the classical:
becomes:
Besides the angular momentum in each direction, we also have the total angular momentum:
Then you have to understand what each one of those does to the each atomic orbital:
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.
Stimulated emission by Ciro Santilli 40 Updated 2025-07-16
Photon hits excited electron, makes that electron go down, and generates a new identical photon in the process, with the exact same:This is the basis of lasers.
Second quantization by Ciro Santilli 40 Updated 2025-07-16
Second quantization also appears to be useful not only for relativistic quantum mechanics, but also for condensed matter physics. The reason is that the basis idea is to use the number occupation basis. This basis is:
Bibliography:
The Roland GR-300 is a guitar synthesizer that was introduced in the late 1970s. It is notable for its ability to convert guitar signal into control voltages to synthesize sound, allowing guitarists to produce a wide range of tones and effects that are typically associated with synthesizers, rather than traditional guitar sounds.
Bernie Krause is a prominent American musician, bioacoustician, and soundscape ecologist known for his work in the field of natural sound and the acoustic environment. He has been a pioneer in recording and studying the sounds of various ecosystems, including forests, wetlands, and oceans. Through his work, Krause has emphasized the importance of natural soundscapes and their role in understanding biodiversity and environmental health.
As of my last update in October 2023, there is no widely recognized technology, product, or concept specifically referred to as "Orion-128." It's possible that it could refer to a project, product, or technology that emerged or gained attention after that date, or it may be a lesser-known or niche term in certain fields.
The geography of Southern and Eastern Serbia is characterized by a diverse landscape that includes mountains, valleys, rivers, and plains. Here are some key features of the region: ### Southern Serbia 1. **Mountain Ranges**: Southern Serbia is home to several mountain ranges, including the Kopaonik and Stara Planina (Old Mountain). Kopaonik is known for its ski resorts and is the highest mountain in Serbia.
SM-1420 is a molecule that has been identified as a potential therapeutic agent for the treatment of neurodegenerative diseases. Specifically, it is a synthetic compound that acts as a modulator of certain cellular pathways involved in neuronal survival and function. Research has suggested that SM-1420 may help in conditions such as Alzheimer's disease and other forms of dementia by promoting neuroprotection and neurogenesis.
Iossif Ostrovskii could refer to a specific individual, potentially in a context such as literature, science, or a related field, though there might not be widely recognized information on such an individual in mainstream sources. It's possible that he could be a lesser-known figure or a contemporary individual not extensively covered until after my last update in October 2023.
Isaak Moiseevich Milin is not a widely recognized figure in public knowledge; however, it is possible that you are referring to a specific individual or specialized topic that may require further context to provide a detailed answer.
Ivan Zhegalkin was a renowned Russian mathematician, known for his contributions to the field of algebra, particularly in the area of polynomial theory and algebraic systems. He is particularly noted for Zhegalkin polynomials, which are used to represent Boolean functions. These polynomials provide a way to express logical functions and have applications in digital circuits and computer science. Zhegalkin's work is significant in abstract algebra and has had a lasting impact on mathematical logic and computer engineering.
Mamadsho Ilolov is a notable figure in the realm of Tajikistan's arts and culture, particularly recognized as a prominent singer and songwriter. He has contributed to the popular music scene in Tajikistan and has gained a following for his performances. Often, his music reflects themes relevant to Tajik culture and traditions.
Sergey Yablonsky is a name that may refer to various individuals or contexts, but it is most commonly associated with a notable figure in the field of music and specifically classical guitar. He is known for his work as a guitarist, composer, and educator. However, without more specific context, it is challenging to provide precise information.
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Vladimir Filippov is a Russian politician known for his involvement in various political roles within the country. He was born on February 5, 1952, and has held significant positions in the Russian government and political landscape. Filippov served as the Minister of Education of the Russian Federation from 1998 until 2004 under President Vladimir Putin's administration.

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!
We have two killer features:
  1. 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-calculus
    Articles 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
  2. 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.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    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.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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