Ciro Santilli @cirosantilli 35

See: Video "Your Life is Your life by Charles Bukowski".

Examples: square, octahedron.

Take $(0,0,0,\dots ,0)$ and flip one of 0's to $\pm 1$. Therefore has $2\times D$ vertices.

Each edge E is linked to every other edge, except it's opposite -E.

On Baidu Baike: baike.baidu.com/item/扇画/8486689

This is perhaps slightly worse than the Tinker Tailor Soldier Spy, but still amazing.

Some difficult points:

The $U(1)$ unitary group is one very over-generalized way of looking at it :-)

A superstar security researcher with some major exploits from in the 2000's.

Analogous problem to the secondary structure of proteins. Likely a bit simpler due to the strong tendency for complementary pairs to bind.

The wave equation contains the entire state of a particle.

From mathematical formulation of quantum mechanics remember that the wave equation is a vector in Hilbert space.

And a single vector can be represented in many different ways in different basis, and two of those ways happen to be the position and the momentum representations.

More importantly, position and momentum are first and foremost operators associated with observables: the position operator and the momentum operator. And both of their eigenvalue sets form a basis of the Hilbert space according to the spectral theorem.

When you represent a wave equation as a function, you have to say what the variable of the function means. And depending on weather you say "it means position" or "it means momentum", the position and momentum operators will be written differently.

This is well shown at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)".

Furthermore, the position and momentum representations are equivalent: one is the Fourier transform of the other: position and momentum space. Remember that notably we can always take the Fourier transform of a function in $L^2$ due to Carleson's theorem.

Then the uncertainty principle follows immediately from a general property of the Fourier transform: en.wikipedia.org/w/index.php?title=Fourier_transform&oldid=961707157#Uncertainty_principle

In precise terms, the uncertainty principle talks about the standard deviation of two measures.

We can visualize the uncertainty principle more intuitively by thinking of a wave function that is a real flat top bump function with a flat top in 1D. We can then change the width of the support, but when we do that, the top goes higher to keep probability equal to 1. The momentum is 0 everywhere, except in the edges of the support. Then:

Bibliography:

The first human-made nuclear chain reaction.

Within the The Holy Trinity of popular Brazilian music, Chico tends to approach the more down to Earth and heavy topics.

The most important publisher, AKA "CRC Jianian". TODO meaning of Jianian?

Discogs entry: www.discogs.com/label/743059-China-Record-Corporation?page=1

Chinese government owned unfortunately.

Their website takes forever to load: www.china-crc.com.cn/, and features mostly Communist shit, and I can't find the decent traditional music listed there.

One thing to try is an Amazon advanced search by label "China Record Co": www.amazon.com/s?i=digital-music&rh=p_33%3AChina+Record+Co&s=relevancerank&Adv-Srch-MP3-Submit.x=42&Adv-Srch-MP3-Submit.y=4&unfiltered=1&ref=sr_adv_m_digital

As always, the best way to get some intuition about an equation is to solve it for some simple cases, so let's give that a try with different fixed potentials.

It is good to watch the Out For blood in Silicon Valley (2019) documentary after this to see how the characters look like in real life. Many feel amazingly cast, very close to the original. The only great exception is the Indian dude, who is completely different. Was it that hard to find some indian dude who looked and felt a little more like the real one?

Mechanics before quantum mechanics and special relativity.