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When the use of LaTeX or MathJax or other typesetting system is not an option, one can still type the braket notation $\left<\psi\right|$ and $\left|\psi\right>$. The simplest way is probably to use the plain "less than" and "greater than" characters found on a typical North American keyboard. However, the results often don't look quite right (to my eyes). One could instead use Unicode characters, such as the "mathematical left angle bracket" (U+27E8, ⟨) and "mathematical right angle bracket" (U+27E9, ⟩) but there are others, such as the "left-pointing angle bracket" (U+2329, 〈) and "right-pointing angle bracket" (U+232A, 〉). (C.f. an answer to a different question in Stack Overflow.) There may be differences in the semantics of these characters that I don't understand, and may have implications for accessibility (e.g., for screen readers).

Are there principled reasons for using a specific set of characters for the angle brackets in braket notation?

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    $\begingroup$ In many situations it's a shibboleth - an author using the right characters as opposed to "<" and ">" might be a way to signal to others that the author is "in the know". $\endgroup$
    – Mark Spinelli
    Jan 18, 2022 at 22:57
  • $\begingroup$ @MarkS Different characters exist because there are semantic or other differences between them. We can take LaTeX as an example: it has distinct commands for what is sometimes visually indistinguishable (e.g., tex.stackexchange.com/questions/122491/difference-of-the-dots). People in technical fields use them, not to signal they're "in the know" (whatever that's supposed to mean) but to communicate more precisely. $\endgroup$
    – mhucka
    Jan 18, 2022 at 23:58

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There is no universally accepted separate mathematical meaning for "$<$" and "$\langle$", if that's what you're asking. Clearly, $<$ is better used for inequalities and similar relational symbols, while $\langle$ is better suited for bra-kets, inner products, etc, but this is mostly about how pretty (and easy to read) the resulting equations are.

If you write an equation like $|1>+|2>$, people will generally know that you mean the same as $|1\rangle+|2\rangle$, it's just that the equation looks ugly. And in latex, the sub-optimal spacing might make for harder-to-read equations in some circumstances.

If you're asking about the difference between things like "〈1|" and "⟨1|", again, people will know what you mean, there is not difference beyond the aesthetics. Math formalism really isn't that fussy about such typesetting differences.

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