Ciro Santilli @cirosantilli 35

Ciro Santilli contributed a bit to this, and was even given push rights, see also: see also: Ciro Santilli's minor projects.

Semi-comical student website to review the toilets of the University of São Paulo. Some of the toilets had a reputation for being terrible.

One is reminded of Crushbridge.

Appears directly on Schrödinger equation! And in particular in the time-independent Schrödinger equation.

The first type of device that allowed sending Morse code without wires, as opposed to the wired electrical telegraph that previously existed.

Naval communications was one of the first major applications, as you can't have wires on boats!

Wireless voice transmission came about with modulation.

The first one Ciro Santilli managed to get working in 2022, and which has a free plan.

You can either verify your sending domain by adding 3 DNS records.

Saw the email on Gmail, but Microsoft Outlook did put it into junk though. Yahoo mail also worked fine.

100 emails a day is not insane, but it is forever and appropriate for a test, I'm happy with that.

Considering e.g. Newton's laws of motion, you take a system that is a function of time $f(t)$, e.g. the position of many point particles, and then you reverse the speeds of all particles, then $f(-t)$ is a solution to that.

Or in other words: symmetric groups are boring, because they are basically everything already!

I like relativistic quantum mechanics.

Best mathematical explanation: Section "Spin comes naturally when adding relativity to quantum mechanics".

Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 3.9 "Elementary particles" has an amazing summary of the preceding chapters the spin value has a relation to the representations of the Lorentz group, which encodes the spacetime symmetry that each particle observes. These symmetries can be characterized by small integer numbers:As usual, we don't know why there aren't elementary particles with other spins, as we could construct them.

Bibliography:

Basically a synonym for doing a large chunk of de novo DNA synthesis.

Double cover of $SO(3)$.

Isomorphic to the quaternions.

Schrödinger equation for a one dimensional particle with $V=0$. The first step is to calculate the time-independent Schrödinger equation for a free one dimensional particle

Then, for each energy $E$, from the discussion at Section "Solving the Schrodinger equation with the time-independent Schrödinger equation", the solution is:Therefore, we see that the solution is made up of infinitely many plane wave functions.

Bibliography: