8:54 AM
This is unrelated to the main issue, but looking at your example, wouldn't \langle and \rangle be a more natural choice than < and >. There is a related TeX.SE question: Braket notation in LaTeX. (Although it is not exactly about this, it seems to be mainly about braket package.) Since this is unrelated to the main question, I'd suggest that we could discuss this further (if needed) in the MathJax chatroom. — Martin Sleziak 44 secs ago

9:18 AM
@MartinSleziak The issue with \langle and \rangle is that they're just characters, so they don't resize to their content. A working alternative is to use \left\langle and \right\rangle to get the same effect as \left< and \right>, but then it's just more characters for the same thing. — Nat 4 mins ago
$\left<0\middle|1\right>$ vs. $\left\langle0\middle|1\right\rangle$
It seems that people usually use \langle:
13

Why are bra and ket defined in the official package braket.sty in two different ways (\bra, \Bra and \ket, \Ket)? I do not understand why there exists the command \bra with non-scalable delimiters. For stylistic reasons, I intuitively used the capital letter versions. Were you ever confronted w...

27

I am using the braket package to generate bra and ket vectors. However, I could not figure out how to do <0|0> using the package. Is there a command for this?

AFAIK $\langle$ and $<$ are different, both as characters and also as far as the category is concerned.
I am not sure how this changes with addition of \left and \right.
@Nat Basically my question is whether \left< and \left\langle really give the same thing.

9:57 AM
@MartinSleziak They definitely appear to be the same thing, as rendered by MathJax. Dunno if another display engine might interpret them differently?

3 hours later…
12:35 PM
4

\langle is smaller and \left< is bigger. But which one should I use in dirac braket and expectation value? Is there a standard practice?

22

Is there any difference between \langle S \rangle and \left< S \right>? Or is \langle just an alias for < that by default works on one line without having to use \left?

The last one seems the most relevant:
> \left<...\right> is an alias for \left\langle ...\right\rangle. These do not do the same thing as \langle ...\rangle! The differences are described in this answer, but the main things are that \left<...\right> scales to its contents and adds extra space sometimes.

12:55 PM
This message from TeX chat room confirms this:
in TeX, LaTeX and Friends, 15 mins ago, by David Carlisle
@MartinSleziak yes < has a delcode that uses the same slot as the \delimiter definition of langle (in latex and plain tex)
@Nat I knew that there is difference between < and \langle which is why I thought that also \left< and \left\langle are different.
So I learned today that they are, in fact, the same (see the links above).
There's a lot of things about TeX and LaTeX I do not know - I am glad that I've learned something new today.
Maybe I'll add also this link - it is the message David Carlisle was responding to:
in TeX, LaTeX and Friends, 21 mins ago, by Martin Sleziak
@MartinSleziak It seems I should have searched better before asking in chat. According to this answer they are the same: "\left<...\right> is an alias for \left\langle ...\right\rangle."