> With quantum mechanics - I know it is not the main focus of Azimuth, so my biggest doubt is what should be the level. Do you think that, as of now, it is OK?
The big challenge of science writing is to carefully imagine a class of readers and always make sure what you write is comprehensible to that class. It doesn't matter so much what the class is, as long as it's much larger than "me, myself, and I".
Can you tell me what class of readers you are trying to be comprehensible to?
Let's see if I can guess from what you write. You write:
|\psi\rangle = \alpha |1\rangle + \beta |2\rangle \equiv
\alpha \\ \beta
Someone who has taken a first course in quantum mechanics will understand the bra-ket notation here. Are you writing to that class of people? Or are you hoping that this equation will explain that notation to someone who has never seen it? That would be overoptimistic, I think.
A mathematically sophisticated reader might see that $\equiv$ sign, realize you're defining $|1 \rangle$ and $|2 \rangle$ by this equation, and take the vertical line and angle bracket in $1 \rangle$ to be undefined primitives. But most mathematicians who haven't seen bra-ket notation will wonder why you're writing things like $| 1 \rangle$ instead of $e_1$ for the standard basis vectors. They will have trouble believing that this vertical line and angle bracket are undefined primitives; they'll want to know the rules governing them. And later you spring the notation $|\psi \rangle$ on the reader, whose meaning cannot be guessed by knowing
$$ |1 \rangle =
1 \\ 0
Quantum mechanics typically takes a year to learn and is considered difficult. So, almost nobody will be able to learn it from a single blog post. Maybe your audience is people who have taken a course on it, or tried to read a book on it, but need more practice?
Will this audience be able to understand the next posts in the series?
Often people overestimate the ability of others to keep up with a rapid ascent from basics to more advanced material. To avoid this problem, sometimes it can be better to choose a fairly sophisticated audience from the start, and write to them. But the main thing is to make a clear choice. It can be very good to say at the start of a post _who your intended audience is_. If the second post is a lot harder than the first, say that. In a blog post you can do this in a jokey way, like
> Now all of a sudden I'll assume you know quantum field theory. If you don't, goodbye - and I hope you had fun!
I do this kind of thing sometimes. It may sound cruel but it's less cruel than suddenly increasing the prerequisites without admitting it.