Ciro Santilli @cirosantilli 40

A good definition is that the sparse matrix has non-zero entries proportional the number of rows. Therefore this is Big O notation less than something that has $N^2$ non zero entries. Of course, this only makes sense when generalizing to larger and larger matrices, otherwise we could take the constant of proportionality very high for one specific matrix.

Of course, this only makes sense when generalizing to larger and larger matrices, otherwise we could take the constant of proportionality very high for one specific matrix.

This is an important metric, because it takes some time for the quantum operations to propagate, and so the depth of a circuit gives you an idea of how long the coherence time a hardware needs to support a given circuit.

Bibliography:

The Dirac equation can be derived basically "directly" from the Representation theory of the Lorentz group for the spin half representation, this is shown for example at Physics from Symmetry by Jakob Schwichtenberg (2015) 6.3 "Dirac Equation".

The Diract equation is the spacetime symmetry part of the quantum electrodynamics Lagrangian, i.e. is describes how spin half particles behave without interactions. The full quantum electrodynamics Lagrangian can then be reached by adding the $U(1)$ internal symmetry.

As mentioned at spin comes naturally when adding relativity to quantum mechanics, this same method allows us to analogously derive the equations for other spin numbers.

Bibliography:

AMO is a slightly more general area than condensed matter physics, including related phenomena with smaller numbers atoms and optics. The two terms are however sometimes used as synonyms. The term AMO has gained wide usage and acceptability, see e.g.:

If Ciro had had greater foresight, this might have been what he studied at university!

The Klein-Gordon equation directly uses a more naive relativistic energy guess of $p^2+m^2$ squared.

But since this is quantum mechanics, we feel like making $p$ into the "momentum operator", just like in the Schrödinger equation.

But we don't really know how to apply the momentum operator twice, because it is a gradient, so the first application goes from a scalar field to the vector field, and the second one...

So we just cheat and try to use the laplace operator instead because there's some squares on it:

But then, we have to avoid taking the square root to reach a first derivative in time, because we don't know how to take the square root of that operator expression.

So the Klein-Gordon equation just takes the approach of using this squared Hamiltonian instead.

Since it is a Hamiltonian, and comparing it to the Schrödinger equation which looks like:taking the Hamiltonian twice leads to:

We can contrast this with the Dirac equation, which instead attempts to explicitly construct an operator which squared coincides with the relativistic formula: derivation of the Dirac equation.

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

Their website, and in particular the recruitment section, are so creepy.

There's not mention of bombs. No photos of atomic explosions. The words "atomic" and "weapon" do not even show up in the front page!!! The acronym AWE is instead used everywhere as an euphemism.

In the recruitment section we can see a bunch of people smiling: web.archive.org/web/20211007213222/https://www.awe.co.uk/careers/working-at-awe/, suggesting:There's even children outreach!!!

Ciro Santilli is not against storing a few nukes to be ready against dictatorships. But don't be such a pussy! Just say what the fuck you are doing more clearly! You are making weapons to kill people and destroy things in order to maintain the Balance of power. If the public can't handle such facts, then shut down the fucking program.

One of the most beautiful molecular machines known!

The first one with such complexity that was uncovered.

The thing rotates like a water wheel for God's sake, except it uses protons instead of water.

The ATP synthase complex is so large that Power, Sex, Suicide by Nick Lane (2006) page 123 contains a cryoEM image of several ATP synthases on small membrane vesicles, this is the paper: pubs.acs.org/doi/abs/10.1021/bi00437a031# under a fucking paywall.