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I find that $\tilde{x} produces a tilde that is much too small for legibility at the screen resolution I normally use for reading. On my screen it looks like a tiny bar above the symbol. This question asked how to generate a larger tilde over a particular wide character (a mathcal W), presumably with the motivation of making the tilde look better matched in size with this large glyph. The answer by Ant provides a couple of methods, which look good for wide characters but bad for narrow ones. Example:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\newcommand{\tildea}[1]{\overset{\sim}{#1}}
\newcommand{\tildeb}[1]{\stackrel{\sim}{\smash{#1}\rule{0pt}{1.1ex}}}

$\tilde{W} \quad \tildea{W} \quad \tildeb{W}$

$\tilde{I} \quad \tildea{I} \quad \tildeb{I}$

\end{document}

Results:

rendered output of latex code

To me the larger tildes over the "I" look like they're way off in terms of horizontal positioning. Is there a way to make a macro that automagically gets this horizontal positioning right, as the \tilde macro seems to do? I would like to avoid having different macros for characters of different widths.

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I can suggest to use the lite version of mtpro2 that you can find to CTAN. Here for example there is a recent documentation (see pag. 14). Is you will use this MWE

\documentclass[12pt]{article}
\usepackage[lite]{mtpro2}
\begin{document}

Let $\wwtilde{I}$ collision be elastic in one frame of reference.\\
Let $\tilde{I}$ and let $ \widetilde{I}$ another frame.

\end{document}

you will obtain this output.

enter image description here

The best tilde is with the command \wwtilde a good solution to center it with any letter. Personally I suggest to leave the same size (or dimension) of "tilde".

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