Issue report at: github.com/ourbigbook/ourbigbook/issues/198 Suppose you had:

programming-language.ciro

= Programming language

\Image[https://raw.githubusercontent.com/cirosantilli/media/master/python-logo.jpg]
{title=The \x[python-programming-language] logo}

== Python
{c}
{disambiguate=programming-language}

logos-i-like.ciro

= Logos I like

\x[image-the-python-logo]

Now, when rendering \x[image-the-python-logo], we would need to fetch two IDs:

But after group all SQL queries together was done, there was no way to know that rendering image-the-python-logo would imply also fetching python-programming-language.

This was solved by adding a new database entry type, REFS_TABLE_X_TITLE_TITLE to the existing References table, which tracks dependencies between IDs.

After this was setup, we can now know that image-the-python-logo depends on image-the-python-logo, and then fetch both of them together in a single JOIN.

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.

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:

See also: en.wikipedia.org/wiki/Measurement_in_quantum_mechanics

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.

This naturally generalizes to Schrödinger equation solution for the hydrogen atom.

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:

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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.

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