Ciro Santilli @cirosantilli 35

One of the main reasons why physicists are obsessed by this topic is that position and momentum are mapped to the phase space coordinates of Hamiltonian mechanics, which appear in the matrix mechanics formulation of quantum mechanics, which offers insight into the theory, particularly when generalizing to relativistic quantum mechanics.

One way to think is: what is the definition of space space? It is a way to write the wave function ${\psi }_x(x)$ such that:And then, what is the definition of momentum space? It is of course a way to write the wave function ${\psi }_p(p)$ such that:

physics.stackexchange.com/questions/39442/intuitive-explanation-of-why-momentum-is-the-fourier-transform-variable-of-posit/39508#39508 gives the best idea intuitive idea: the Fourier transform writes a function as a (continuous) sum of plane waves, and each plane wave has a fixed momentum.

Bibliography:

There's nothing like seeing the hypocrisy of the "Liberté, Égalité, Fraternité" people destroyed.

Interesting how Algeria now supports China's Xinjiang policy in 2019. But of course, dictatorships tend to work together

Ciro Santilli's father, an avid history reader, and in particular interested in the military dictatorship in Brazil through which he lived, once told Ciro how the French torture doctrine was directly adopted by Brazillian military, e.g. then even invited general Paul Aussaresses who had served in Algeria, to help them out with intelligence operations and give courses. Bro, fuck that.

But of course, the Americans weren't too far behind in Guantanamo.

NIST database for spectral line: physics.nist.gov/PhysRefData/ASD/lines_form.html

Let's do a sanity check.

Searching for "H" for hydrogen leads to: physics.nist.gov/cgi-bin/ASD/lines1.pl?spectra=H&limits_type=0&low_w=&upp_w=&unit=1&submit=Retrieve+Data&de=0&format=0&line_out=0&en_unit=0&output=0&bibrefs=1&page_size=15&show_obs_wl=1&show_calc_wl=1&unc_out=1&order_out=0&max_low_enrg=&show_av=2&max_upp_enrg=&tsb_value=0&min_str=&A_out=0&intens_out=on&max_str=&allowed_out=1&forbid_out=1&min_accur=&min_intens=&conf_out=on&term_out=on&enrg_out=on&J_out=on

From there we can see for example the 1 to 2 lines:

We see that the table is sorted from lower from level first and then by upper level second.

So it is good to see that we are in the same 121nm ballpark as mentioned at hydrogen spectral line.

TODO why I can't see 2s to 2p transitions there to get the fine structure?

Split in the spectral line when a magnetic field is applied.

Non-anomalous: number of splits matches predictions of the Schrödinger equation about the number of possible states with a given angular momentum. TODO does it make numerical predictions?

Anomalous: evidence of spin.

www.pas.rochester.edu/~blackman/ast104/zeeman-split.html contains the hello world that everyone should know: 2p splits into 3 energy levels, so you see 3 spectral lines from 1s to 2p rather than just one.

p splits into 3, d into 5, f into 7 and so on, i.e. one for each possible azimuthal quantum number.

It also mentions that polarization effects become visible from this: each line is polarized in a different way. TODO more details as in an experiment to observe this.

Well explained at: Video "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)".

A subset of Spacetime diagram.

The key insights that it gives are:

Discrete quantum system model that can model both spin in the Stern-Gerlach experiment or photon polarization in polarizer.

Also known in quantum computing as a qubit :-)

Claims provably fair. satoshidice.com/fair clarifies what that means: they prove fairness by releasing a hash of the seed before the bets, and the actual seed after the bets.

As mentioned in bitcoin.it, it functions basically as cryptocurrency tumbler in practice.