Starting in the 2019 redefinition of the SI base units, the elementary charge is assigned a fixed number, and the Ampere is based on it and on the second, which is beautiful.
This choice is not because we attempt to count individual electrons going through a wire, as it would be far too many to count!
Rather, it is because because there are two crazy quantum mechanical effects that give us macroscopic measures that are directly related to the electron charge. www.nist.gov/si-redefinition/ampere/ampere-quantum-metrology-triangle by the NIST explains that the two effects are:
Those effect work because they also involve dividing by the Planck constant, the fundamental constant of quantum mechanics, which is also tiny, and thus brings values into a much more measurable order of size.
Schrödinger picture by Ciro Santilli 40 Updated 2025-07-16
To better understand the discussion below, the best thing to do is to read it in parallel with the simplest possible example: Schrödinger picture example: quantum harmonic oscillator.
The state of a quantum system is a unit vector in a Hilbert space.
"Making a measurement" for an observable means applying a self-adjoint operator to the state, and after a measurement is done:
Those last two rules are also known as the Born rule.
Self adjoint operators are chosen because they have the following key properties:
Perhaps the easiest case to understand this for is that of spin, which has only a finite number of eigenvalues. Although it is a shame that fully understanding that requires a relativistic quantum theory such as the Dirac equation.
The next steps are to look at simple 1D bound states such as particle in a box and quantum harmonic oscillator.
The solution to the Schrödinger equation for a free one dimensional particle is a bit harder since the possible energies do not make up a countable set.
This formulation was apparently called more precisely Dirac-von Neumann axioms, but it because so dominant we just call it "the" formulation.
Quantum Field Theory lecture notes by David Tong (2007) mentions that:
if you were to write the wavefunction in quantum field theory, it would be a functional, that is a function of every possible configuration of the field .
A speaker terminal is a connector or binding point on a speaker where audio cables are attached to enable the transmission of sound signals from an amplifier or audio source to the speaker. Speaker terminals can vary in design and type, but they generally fall into a few common categories: 1. **Binding Posts**: These are typically found on higher-end speakers and allow the use of banana plugs, spade connectors, or bare wire. They offer a secure and reliable connection.
South African bioinformaticians are scientists and researchers who specialize in the field of bioinformatics within South Africa. Bioinformatics is an interdisciplinary field that combines biology, computer science, mathematics, and statistics to analyze and interpret biological data, particularly genetic and genomic information. In South Africa, bioinformaticians may work in various sectors, including academic institutions, research organizations, healthcare, agriculture, and biotechnology companies.
Speck Electronics is a company known for designing and manufacturing various electronic devices and accessories. While they are particularly recognized for their mobile phone cases and protective accessories, they may also produce other types of consumer electronics. Their products typically focus on combining functionality with style, offering consumers choices that cater to both aesthetic and practical needs. For the most accurate and up-to-date information, it's advisable to visit the official Speck Electronics website or check recent news sources.
Spectral Band Replication (SBR) is a technique used in audio coding and compression, particularly in the context of lossy compression formats like AAC (Advanced Audio Codec). The primary goal of SBR is to enhance the perceived audio quality while keeping the file size relatively small. ### How it Works: 1. **High-Frequency Extension**: SBR is primarily used to reconstruct high-frequency content that can be difficult to encode at lower bit rates.
As of my last knowledge update in October 2021, there is no widely known concept, theory, or person specifically referred to as "Denis Higgs." It might refer to a lesser-known individual or be a misspelling or variation of "Higgs," which is often associated with the Higgs bosona particle in physics that is part of the Standard Model and was discovered in 2012.
Schulpfontein is a small settlement located in the Northern Cape province of South Africa. Like many places in this region, it is characterized by its rural setting and is part of the larger municipal governance structures in the area. The economy of such settlements often revolves around agriculture and livestock farming.
Valandovo Municipality is a local government area located in the southeastern region of North Macedonia. The municipality encompasses the town of Valandovo, which serves as its administrative center, along with several surrounding villages. Valandovo is known for its agricultural activities, particularly in the cultivation of various crops and fruit, owing to the favorable climate and fertile land in the area. The region has a rich cultural heritage, featuring a blend of traditional customs and modern influences.
Struga Municipality is a municipality located in the southwestern part of North Macedonia, particularly known for its picturesque landscapes and the presence of the city of Struga, which serves as its administrative center. The municipality is situated along the shores of Lake Ohrid, one of the oldest and deepest lakes in Europe, which is a UNESCO World Heritage site. Struga is notable for its cultural and historical significance, with various festivals, traditions, and attractions.
Anatoly Maltsev is known as a Russian professional wrestler and coach, specializing in sambo and judo. He has contributed to the development of these sports in Russia and beyond.
Leonid I. Vainerman is a mathematician known for his contributions to various fields within mathematical sciences, particularly in areas such as differential equations, mathematical modeling, and applied mathematics. However, details specific to his accomplishments, publications, or research interests can vary, and additional context is needed for a more comprehensive overview.
As of my last update in October 2023, Rifkat Bogdanov is not a widely recognized name in public discourse, literature, or other prominent contexts. It's possible that he could be a figure who has gained relevance in a specific field unrecorded in widespread sources or is a private individual.
As of my last knowledge update in October 2023, Sergey Chesnokov does not appear to be a widely recognized public figure, historical figure, or significant entity in popular culture. It’s possible that he could be a private individual, a professional in a specific field, or a name that has gained prominence after my last update.
As of my last update in October 2023, there isn't any widely known or notable figure, concept, or entity named "Oleg Tozoni." It's possible that he could be a private individual or involved in a niche area that hasn't gained significant public attention.
As of my last knowledge update in October 2021, there isn't a widely known public figure or entity specifically named Kirill Gurov. It's possible that Kirill Gurov might be a private individual, a character in a story, or someone who has gained recognition after that date.

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