A specific format for nice tables

see, if the following solution is close to what you after:

\documentclass[a4paper,12pt]{article} % <---
\usepackage{mathtools,amssymb}                % <---
\usepackage{booktabs, 
            makecell}                         % <---
\setcellgapes{3pt}                            % <---
\usepackage{isotope}
\usepackage[table]{xcolor}                    % <---
\arrayrulecolor{teal}                         % <--- 

\usepackage[skip=1ex]{caption}                % <---
    \DeclareCaptionFont{teal}{\color{teal}}   % <---
    \captionsetup[table]{font=bf,             % <---
                         labelfont={teal,bf},
                         singlelinecheck=off}

\begin{document}
    \begin{table}[htb]              % <---
    \makegapedcells                 % <---
    \caption{My fancy table}        % <---
\begin{tabular}{l*{2}{>{$}c<{$}}}   % <---
    \toprule[2pt]                   % toprule thickens you can change according 
                                    % to your taste, for example to 3pt or more
\textbf{Osservabile} & \textbf{Simbolo} & \textbf{Operatore associato}  \\
    \midrule
Posizione           & \bar{r}       & \bar{r}                           \\
Momento             & \bar{p}       & -i\hslash \overline \nabla        \\
Energia potenziale  & \mathcal{U}   & \mathcal{U}(r)                    \\
Energia cinetica    & \mathcal{K}   & -\dfrac{\hslash^2}{2m}\nabla^2    \\
Hamiltoniana        & H             & -\dfrac{\hslash^2}{2m}\nabla^2+\mathcal{U}(r) \\
Energia totale      & E             & -i\hslash\dfrac{\partial}{\partial t}         \\
    \bottomrule
\end{tabular}
    \end{table}

    \begin{table}[htb]
    \caption{My another fancy table}
\makegapedcells
\begin{tabular}{cccc}
    \toprule[2pt]      % <---
\thead{Numeri\\ di massa}     
        & \thead{Elemento\\ chimico}     
                        & \thead{Prodotto\\ iniziale}   
                                                    & \thead{Prodotto\\ finale}\\   % <---
    \midrule
$4n$    &  Torio        &   \isotope[232][90]{Th}   &   \isotope[208][82]{Pb}   \\
$4n+1$  &  Neptunio     &   \isotope[237][93]{Np}   &   \isotope[209][83]{Bi}   \\
$4n+2$  &  Uranio       &   \isotope[238][92]{U}    &   \isotope[206][82]{Pb}   \\
$4n+3$  &  Attinio      &   \isotope[235][92]{U}    &   \isotope[207][82]{Pb}   \\
    \bottomrule
\end{tabular}
    \end{table}

\end{document}

so far i consider only tables in your mwe (it not contain your table 13.1, if you will provide code for this table content, i will show solution example for it too)

edit: differences between above and your mwe are indicated by % <---. as you can see, above are added packages xcolor for coloring table rules as well font for tables' labels, makecell for adding more vertical spaces around cells contents and for macro \thead, which enable to write column heads in two (or more, if necessary) lines, caption for defining caption style (font family and color, positioning of caption).

in above mwe tables are not horizontally centered. if you like to have them centered, just add \centering after \begin{table}[...]. but in this case the caption will be aligned with left text border. for aligning it width beginning of table, you should use threeparttable as shown in mwe below. in it is also added a way how to select font used in caption and have upper case font in caption label (indicaed by % <===). so far i select iwona, but you can replace it with font of your wish. also the thikness of rules are defined globally.

\documentclass[a4paper,12pt,italian]{article}
\usepackage{babel}
\usepackage{mathtools,amssymb}
\usepackage{booktabs, makecell, 
            threeparttable}       % <---
\setlength\heavyrulewidth{2pt}    % <---
\setlength\lightrulewidth{1.2pt}  % <---

\setcellgapes{3pt}
\renewcommand\theadfont{\normalsize\bfseries}
\renewcommand\theadgape{}

\usepackage{isotope}
\usepackage[table]{xcolor}
\arrayrulecolor{teal}
\usepackage[skip=0.5ex]{caption}
    \DeclareCaptionLabelFormat{uc}{\MakeUppercase{#1}~#2}                % <===
    \DeclareCaptionFont{teal}{\color{teal}\fontfamily{iwona}\selectfont} % <===
    \captionsetup[table]{font={large,teal,bf},
                         labelformat=uc,                                 % <===
                         singlelinecheck=off}                               

%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%

\begin{document}
    \begin{table}[htb]
    \centering                  % <---
   \begin{threeparttable}       % <---
    \caption{My fancy table}
\makegapedcells
\begin{tabular}{l*{2}{>{$}c<{$}}}
    \toprule
\textbf{Osservabile} & \textbf{Simbolo} & \textbf{Operatore associato}  \\
    \midrule
Posizione           & \bar{r}       & \bar{r}                           \\
Momento             & \bar{p}       & -i\hslash \overline \nabla        \\
Energia potenziale  & \mathcal{U}   & \mathcal{U}(r)                    \\
Energia cinetica    & \mathcal{K}   & -\dfrac{\hslash^2}{2m}\nabla^2    \\
Hamiltoniana        & H             & -\dfrac{\hslash^2}{2m}\nabla^2+\mathcal{U}(r) \\
Energia totale      & E             & -i\hslash\dfrac{\partial}{\partial t}         \\
    \bottomrule
\end{tabular}
    \end{threeparttable}        % <---
    \end{table}

    \begin{table}[htb]
    \centering                  % <---
   \begin{threeparttable}       % <---
    \caption{My another fancy table}
\makegapedcells
\begin{tabular}{cccc}
    \toprule
\thead{Numeri\\ di massa}
        & \thead{Elemento\\ chimico}
                        & \thead{Prodotto\\ iniziale}
                                                    & \thead{Prodotto\\ finale}\\
    \midrule
$4n$    &  Torio        &   \isotope[232][90]{Th}   &   \isotope[208][82]{Pb}   \\
$4n+1$  &  Neptunio     &   \isotope[237][93]{Np}   &   \isotope[209][83]{Bi}   \\
$4n+2$  &  Uranio       &   \isotope[238][92]{U}    &   \isotope[206][82]{Pb}   \\
$4n+3$  &  Attinio      &   \isotope[235][92]{U}    &   \isotope[207][82]{Pb}   \\
    \bottomrule
\end{tabular}
    \end{threeparttable}        % <---
    \end{table}
\end{document}

which gives:

(red lines indicate page borders)

• \arrayrulecolor from the colortbl package for the rule color
• captionsetep and captionof commands from the caption package for the caption settings
• toprule[3pt] for a top rule 3pt thick
• \renewcommand{\arraystretch}{1.5} for increasing row size by a factor of 1.5
• To get the table centered and the caption starting at the table left limit: Put the table content inside a minipage environment of width equal to the table width then put the minipage inside a center environment

!

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\usepackage{booktabs, isotope,colortbl,caption}

\arrayrulecolor{cyan}
\captionsetup[table]{labelfont={color=cyan,sc},justification=RaggedRight,singlelinecheck=false,skip=2pt}

\newlength{\mytablewidth}
\newsavebox{\mytablebox}

 \renewcommand{\arraystretch}{1.5}

\begin{document}
\begin{center}
\savebox{\mytablebox}
{\begin{tabular}{lcc} 
\toprule[3pt]
\textbf{Osservabile} & \textbf{Simbolo} & \textbf{Operatore associato} \\
\toprule
Posizione & $\bar{r}$ & $\bar{r}$ \\
Momento & $\bar{p}$ & $-i\hslash \overline \nabla$ \\
Energia potenziale & $  \mathcal{U}$ &  $\mathcal{U}(r)$ \\
Energia cinetica & $\mathcal{K}$ &  $-\dfrac{\hslash^2}{2m}\nabla^2$ \\
Hamiltoniana & $H$ & $-\dfrac{\hslash^2}{2m}\nabla^2+\mathcal{U}(r)$\\
Energia totale & $E$ & $-i\hslash\dfrac{\partial}{\partial t}$\\
\bottomrule
\end{tabular}}
\settowidth{\mytablewidth}{\usebox{\mytablebox}}
\begin{minipage}{\mytablewidth}
\captionof{table}{my first table}
\usebox{\mytablebox}
\end{minipage}
\end{center}
\vskip 1cm
\begin{center}
\savebox{\mytablebox}{\begin{tabular}{cccc}
\toprule[3pt]
\textbf{Numeri di massa} & \textbf{Elemento chimico} & \textbf{Prodotto iniziale} & \textbf{Prodotto finale}\\
\midrule
$4n$ &  Torio   &   \isotope[232][90]{Th} &   \isotope[208][82]{Pb} \\
$4n+1$ &  Neptunio   &  \isotope[237][93]{Np}  &  \isotope[209][83]{Bi}  \\
$4n+2$ &  Uranio   &  \isotope[238][92]{U}  & \isotope[206][82]{Pb}  \\
$4n+3$ &  Attinio   &  \isotope[235][92]{U}  &  \isotope[207][82]{Pb} \\
\bottomrule
\end{tabular}}

\settowidth{\mytablewidth}{\usebox{\mytablebox}}
\begin{minipage}{\mytablewidth}
\captionof{table}{my second table}
\usebox{\mytablebox}
\end{minipage}

\end{center}
\end{document}