Dirac notation

Quantum mechanics writes states as kets, their duals as bras, and inner products as bracketed pairs. Building the notation by hand from \langle, |, and \rangle works, but it is tedious and the delimiters do not grow with the contents. The braket package provides commands that assemble the notation and size everything to fit.

\usepackage{braket}
\braket{\psi|\phi}
\braket{\psi|A|\phi}
\set{\vec{x}|x > 0}

What each command does

\braket{\psi|\phi} sets the full inner product: angle brackets on the outside, a vertical bar between the two states, all matched in height. With two bars, \braket{\psi|A|\phi} becomes the matrix element of the operator A between the two states, the form at the heart of every expectation value and perturbation calculation. The package also provides \bra{\psi} and \ket{\phi} for the two halves on their own; a bare ket is the usual way to name a state in prose.

\set{\vec{x}|x > 0} is a bonus from the same package: set-builder notation with braces and a middle bar, useful well beyond physics.

The sizing is the real argument for the package. Put a fraction or a sum inside \braket and the brackets and bars stretch to match, exactly where a hand-built \langle ... \rangle needs \left and \right on every delimiter and still tends to drift out of proportion.

Alternatives and neighbors

The physics package offers a similar set, including \bra, \ket, \ev for expectation values, and \mel for matrix elements, alongside shorthands for derivatives and commutators. Both packages define \bra and \ket, so pick one per document rather than loading both. In a template where you cannot add packages, \langle \psi | \phi \rangle with \left/\right around tall contents produces the same output with more typing.

For Feynman diagrams, which often live in the same documents, packages such as tikz-feynman build on TikZ; that is a separate drawing skill, closer in spirit to commutative diagrams than to anything on this page.

The common mistake is typing <\psi|\phi> with the keyboard’s angle characters. Those are the less-than and greater-than relations, so LaTeX spaces them as comparisons and draws them at the wrong height. Real Dirac brackets come from \langle and \rangle or, better, from the commands above. The difference is obvious the moment you set both forms next to each other in the live playground.