Ciro Santilli @cirosantilli 37

The third one of the University of California after UC Berkeley and UCLA.

Brother of Saint Peter, called by Jesus in fishers of men. Crucified.

Take the group of all Translation in ${\mathbb{R}}^1$.

Let's see how the generator of this group is the derivative operator:

The way to think about this is:

So let's take the exponential map:and we notice that this is exactly the Taylor series of $f(x)$ around the identity element of the translation group, which is 0! Therefore, if $f(x)$ behaves nicely enough, within some radius of convergence around the origin we have for finite $x_0$:

This example shows clearly how the exponential map applied to a (differential) operator can generate finite (non-infinitesimal) Translation!

Dropped in favor of SVG 2.

Good shortcuts and user experience.

No waveform viewer: github.com/otsaloma/gaupol/issues/49 so unusable.

Leads to the Klein-Gordon equation.

Originally done with (neutral) silver atoms in 1921, but even clearer theoretically was the hydrogen reproduction in 1927 by T. E. Phipps and J. B. Taylor.

The hydrogen experiment was apparently harder to do and the result is less visible, TODO why: physics.stackexchange.com/questions/33021/why-silver-atoms-were-used-in-stern-gerlach-experiment

Just ignore the electron electron interactions.

Bibliography:

www.youtube.com/watch?v=6DxlkxA82FM COVID-19 Symposium: Entry of Coronavirus into Cells | Dr. Paul Bates

Interaction points:

In the case of the Schrödinger equation solution for the hydrogen atom, each orbital is one eigenvector of the solution.

Remember from time-independent Schrödinger equation that the final solution is just the weighted sum of the eigenvector decomposition of the initial state, analogously to solving partial differential equations with the Fourier series.

This is the table that you should have in mind to visualize them: en.wikipedia.org/w/index.php?title=Atomic_orbital&oldid=1022865014#Orbitals_table

TODO understand a bit more intuitively.