Slightly rounded angle brackets

How would be possible to get angle brackets with a slightly rounded angle? Here's a handwritten example of the desired result.

• Welcome to tex.sx. I'm finding it hard to visualize what you want. A hand-drawn example would help. – barbara beeton Feb 1 at 22:17
• Thank you. I'll add the example! – Giafazio Feb 2 at 15:05

After some research I found that a result close enough to the original idea could be obtained using tikz.

\documentclass{article}
\usepackage{xparse}
\usepackage{amsmath}
\usepackage{tikz}

\newcommand{\lroungle}{\mathrel{\mkern-4mu
\raisebox{-2.1pt}{%
\tikz[line cap=round, line join=round]
\draw
(0ex, 2.2ex) to[out=-135,in=135, distance=7]     (0ex,0ex)
;%
}\mkern-3mu}
}
\newcommand{\rroungle}{%
\mathrel{\mkern-4mu\raisebox{-2.1pt}{%
\tikz[line cap=round, line join=round]
\draw
(0ex, 2.2ex) to[out=-45,in=45, distance=7]   (0ex,0ex)
;%
}}
}
\begin{document}
$\lroungle A , B \rroungle$
\end{document}


Moreover, I noticed that one could slightly modify the braket commands in the physics package to substitute the standard angle brackets with the rounded ones.

\documentclass{article}
\usepackage{xparse}
\usepackage{amsmath, amsfonts}
\usepackage{tikz, scalerel}

\newcommand{\lroungle}{\mathrel{\mkern-4mu
\raisebox{-2.1pt}{%
\tikz[line cap=round, line join=round]
\draw
(0ex, 2.2ex) to[out=-135,in=135, distance=7]     (0ex,0ex)
;%
}\mkern-3mu}
}
\newcommand{\rroungle}{%
\mathrel{\mkern-4mu\raisebox{-2.1pt}{%
\tikz[line cap=round, line join=round]
\draw
(0ex, 2.2ex) to[out=-45,in=45, distance=7]   (0ex,0ex)
;%
}}
}

\DeclareDocumentCommand\rbra{ s m t\rket s g }
{ % Bra
\IfBooleanTF{#3}
{ % Contraction
\IfBooleanTF{#1}
{ % Bra has a star: no resize
\IfNoValueTF{#5}
{\rbraket*{#2}{} \IfBooleanTF{#4}{*}{}}
{\rbraket*{#2}{#5}}
}
{
\IfBooleanTF{#4}
{ % Ket has a star: no resize
\IfNoValueTF{#5}
{\rbraket{#2}{} *}
{\rbraket*{#2}{#5}}
}
{\rbraket{#2}{\IfNoValueTF{#5}{}{#5}}} % Neither term is starred: auto sizing
}
}
{ % No contraction
\IfBooleanTF{#1}
{\lroungle \smash{#2} \rvert}
{\stretchleftright{\lroungle\mkern2.5mu}{#2}{\rvert}}
\IfBooleanTF{#4}{*}{}
\IfNoValueTF{#5}{}{#5}
}
}

\DeclareDocumentCommand\rket{ s m }
{ % Ket
\IfBooleanTF{#1}
{\vphantom{#2}\lvert\smash{#2}\rroungle} % No resize
{\stretchleftright{\lvert}{#2}{\mkern2.5mu\rroungle}} % Auto sizing
}

\DeclareDocumentCommand\rinnerproduct{ s m g }
{ % Inner product
\IfBooleanTF{#1}
{ % No resize
\IfNoValueTF{#3}
{\vphantom{#2}\lroungle\smash{#2}\vert\smash{#2}\rroungle}
{\vphantom{#2#3}\lroungle\smash{#2}\vert\smash{#3}\rroungle}
}
{ % Auto resize
\IfNoValueTF{#3}
{\stretchleftright{\lroungle}{#2}{\vert} #2 \stretchrel*{\rroungle}
{\vphantom{#2}}}
{\stretchleftright{\lroungle}{#2 \vphantom{#3}}{\vert} {#3}\stretchrel*
{\rroungle}{\vphantom{#2#3}}}
}
}
\DeclareDocumentCommand\rbraket{}{\rinnerproduct}

\begin{document}
\newcommand{\kkt}{\widetilde{\mathbf k}}
\newcommand{\eps}{\varepsilon}
\begin{equation*}
\sum_{\mathbf k \in 2\pi \mathbf{Z}^3} \rket*{\mathbf k}\rbra*{\mathbf k}=\mkern-8mu \sum_{\kkt \in 2\pi\eps \mathbf{Z}^3}\rket{\frac{\kkt}{\eps}} \rbra{\frac{\kkt}{\eps}}
\end{equation*}
\end{document}


• I have not understood. Excuse me. +1 for you. – Sebastiano Feb 3 at 21:56