3
$\begingroup$

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?

$\endgroup$
2
  • 1
    $\begingroup$ 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". $\endgroup$ 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

1 Answer 1

2
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.