Ciro Santilli @cirosantilli 37

A pair of Austrailan deep learning training provider/consuntants that have produced a lot of good free learning materials:Authors:

The transpose and matrix inverse commute:

Was a direct tech predecessor to the iPhone.

Determines what can or cannot happen when multiple queries are running in parallel.

See Section "SQL transaction isolation level" for the most common context under which this is discussed: SQL.

Subtle is the Lord by Abraham Pais (1982) page 85:so it is quite cool to see that organic chemistry is one of the things that pushed atomic theory forward. Because when you start to observe that isomers has different characteristics, despite identical proportions of atoms, this is really hard to explain without talking about the relative positions of the atoms within molecules!

TODO: is there anything even more precise that points to atoms in stereoisomers besides just the "two isomers with different properties" thing?

Converts DNA to RNA.

Databases and projects:

Before reading any further, you must understand heat equation solution with Fourier series, which uses separation of variables.

Once that example is clear, we see that the exact same separation of variables can be done to the Schrödinger equation. If we name the constant of the separation of variables $E$ for energy, we get:

Because the time part of the equation is always the same and always trivial to solve, all we have to do to actually solve the Schrodinger equation is to solve the time independent one, and then we can construct the full solution trivially.

Once we've solved the time-independent part for each possible $E$, we can construct a solution exactly as we did in heat equation solution with Fourier series: we make a weighted sum over all possible $E$ to match the initial condition, which is analogous to the Fourier series in the case of the heat equation to reach a final full solution:

The fact that this approximation of the initial condition is always possible from is mathematically proven by some version of the spectral theorem based on the fact that The Schrodinger equation Hamiltonian has to be Hermitian and therefore behaves nicely.

It is interesting to note that solving the time-independent Schrodinger equation can also be seen exactly as an eigenvalue equation where:The only difference from usual matrix eigenvectors is that we are now dealing with an infinite dimensional vector space.

Furthermore:

Bibliography:

This game was mind blowing to Ciro Santilli and all kids. It felt so real. The perfect contrast between peaceful town work and saving the world. OMG.