Ciro Santilli @cirosantilli 37

Notation used in quantum mechanics.

Ket is just a vector. Though generally in the context of quantum mechanics, this is an infinite dimensional vector in a Hilbert space like $L^2$.

Bra is just the dual vector corresponding to a ket, or in other words projection linear operator, i.e. a linear function which can act on a given vector and returns a single complex number. Also known as... dot product.

For example:is basically a fancy way of saying:that is: we are taking the projection of $y$ along the $x$ direction. Note that in the ordinary dot product notation however, we don't differentiate as clearly what is a vector and what is an operator, while the bra-ket notation makes it clear.

The projection operator is completely specified by the vector that we are projecting it on. This is why the bracket notation makes sense.

It also has the merit of clearly differentiating vectors from operators. E.g. it is not very clear in $x\cdot y$ that $x$ is an operator and $y$ is a vector, except due to the relative position to the dot. This is especially bad when we start manipulating operators by themselves without vectors.

This notation is widely used in quantum mechanics because calculating the probability of getting a certain outcome for an experiment is calculated by taking the projection of a state on one an eigenvalue basis vector as explained at: Section "Mathematical formulation of quantum mechanics".

Making the projection operator "look like a thing" (the bra) is nice because we can add and multiply them much like we can for vectors (they also form a vector space), e.g.:just means taking the projection along the $x+y$ direction.

Ciro Santilli thinks that this notation is a bit over-engineered. Notably the bra's are just vectors, which we should just write as usual with $\overrightarrow{v}$... the bra thing makes it look scarier than it needs to be. And then we should just find a different notation for the projection part.

Maybe Dirac chose it because of the appeal of the women's piece of clothing: bra, in an irresistible call from British humour.

But in any case, alas, we are now stuck with it.

Poet warriors monkeys? Or Code peasants (码农) according to the Chinese.

Ciro Santilli claims to be one of them.

Much like a pianist plays his piano, a software engineer plays his computer.

Too many fun skit videos for Ciro Santilli's taste, but does have some serious derivations in quantum electrodynamics.

The Portuguese term for it is "música popular brasileira". The widely recognized Brazilian acronym is "MPB".

"Brazilian pop" and "Br-pop" are inventions by Ciro Santilli, which are how Ciro thinks Brazil should market it to the world.

Unfortunately "B-pop" is too ambiguous with British pop music, and should be avoided.

YouTube playlist by Ciro Santilli containing all the songs in this section: www.youtube.com/playlist?list=PLcZOZrP1P_V4_SBDnegcLTcP-5YhNmWBB

Bibliography:

Self promoted at:Not self-promoted at:

List of handbooks open as of 2022 at: www.maths.ox.ac.uk/members/students/undergraduate-courses/teaching-and-learning/handbooks-synopses Kudos, e.g. unlike the physics course of the University of Oxford which paywalled them. 2022 one: www.maths.ox.ac.uk/system/files/attachments/UG%20Handbook%202022.pdf

The Oxford mathematics Moodle has detailed course listings, and most PDFs are not paywalled.

E.g. the 2024 course:

This is a good approach. The downside is that while you are developing the implementation and testing interactively you might notice that the requirements are wrong, and then the tests have to change.

One intermediate approach Ciro Santilli likes is to do the implementation and be happy with interactive usage, then create the test, make it pass, then remove the code that would make it pass, and see it fail. This does have a risk that you will forget to test something, but Ciro finds it is a worth it generally. Unless it really is one of those features that you are unable to develop without an automated test, generally more "logical/mathematical" stuff. This is a sort of laziness Driven Development.

Reactor of the Hanford site of the produced the plutonium used for Trinity and Fat Man.

This was the first full scale nuclear reactor in the world, and was brought up slowly to test it out.

There is a lot of "who kills who" useless fluff, and everything to do with the wife is boring, but too much gold otherwise.

It is amazing to see how seasons got better and better until the finale. The last season was amazing, Ciro Santilli actually watched all episodes of that one! This is clearly seen on the evolution of metacritic scores.