How to render a "double" ket

Question

I am hoping to render something similar to a ket (from the braket package), but where each line is 'doubled'. For example, something similar to this:

I would like it to...

• stretch vertically to contain the contents, like \ket{x} does
• have subscripts placed below it in the same location that \ket{x}_n prescribes.

Here are some insufficient attempts (both using commands from the braket package):

• \ket{\ket{x}}. It looks like this:

  

  Blegh!

• \| x \rangle!\rangle. It looks like the first image in this post, but it doesn't scale vertically, and it doesn't place subscripts in the right location.

  E.g. \| \frac{x}{y} \rangle\!\rangle looks like

  

  and \| x \rangle!\rangle_y looks like

  

• \ket{\!\ket{x}\hspace{-2.7pt}}. This renders okay, but the spacing between the lines varies with the height of the contents.

  

How can I achieve something visually similar to \|x\rangle!\rangle but which correctly stretches vertically to contain its contents, and which places subscripts at the same vertical position as \ket{x}? This will be used exclusively in math environments.

Answer 1

In amssymb and most other packages, ‖ is \Vert, which also has the aliases \lVert for \mathopen{Vert} and \rVert for \mathclose{Vert}.

Many packages define the ⟫ math symbol as \rAngle, and a few as \rrangle. There is similarly a \lAngle. This works with unicode-math, or see the Comprehensive LaTeX Symbols list for legacy 8-bit packages. You do not want to use the French-style quotation marks, as those will not properly scale in math mode.

The macros for paired, sized delimiters in mathtools are very handy for this.

\documentclass{article}
\usepackage{mathtools}
\usepackage{newcomputermodern} % Or stix2, etc.
\DeclarePairedDelimiter{\Bra}{\lAngle}{\rVert}
\DeclarePairedDelimiter{\Ket}{\lVert}{\rAngle}
\begin{document}
[ \Bra*{\frac{x^2}{2}} ; \Ket{y} ; \Ket[\big]{x_i^n}
]
\end{document}

The newcomputermodern package needs LuaLaTeX or XeLaTeX, but you can substitute your font package of choice.

If you need a three-argument double bra-ket which scales its inner delimiters, there is a code sample in section 3.6 of the mathtools manual.

Answer 2

I got some inspiration from this nice answer and came up with this approach:

\documentclass{article}
\newsavebox{\mstrut}
\newcommand{\bbra}[1]{%
    \sbox{\mstrut}{(#1)}%
    \mathinner{\left\langle\kern-0.5\ht\mstrut\left\langle{#1}\right|\mkern-2mu\right|}%
}
\newcommand{\kett}[1]{%
    \sbox{\mstrut}{(#1)}%
    \mathinner{\left|\mkern-2mu\left|{#1}\right\rangle\kern-0.5\ht\mstrut\right\rangle}%
}
\begin{document}
$\bbra{x}_n$
$\kett{x}_n$
$\bbra{\frac{x}{y}}_n$
$\kett{\frac{x}{y}}_n$
\end{document}