[Tex/LaTex] missing $ inserted .\end{frame}

beamermath-mode

  \begin{frame}{Calcolo classico}

       \vspace{-1cm}

    \begin{equation*}

    mv = \dfrac{E_{\gamma}}{c} + m(v-v_{R}); \qquad
       E_{e} + \dfrac{1}{2}mv^{2} = E_{f} + E_{\gamma} + \dfrac{1}{2}m(v-v_{R})^{2}\\
   \vspace{0.1cm}
         \textcolor{blue}{Ponendo:}\\
        E_{R} = \dfrac{1}{2}mv_{R}^{2} = \dfrac{E_{\gamma}^{2}}{2mc^{2}} \approx \dfrac{E_{0}^{2}}{2mc^{2}}; \qquad
        \vspace{0.1cm}
        E_{D} = mvv_{R} = \dfrac{E_{\gamma}v}{c} \approx  \dfrac{E_{0}v}{c}\\
           \vspace{0.1cm}
       \textcolor{blue}{ Otteniamo:}\\

        E_{\gamma}= E_{0} -E_{R} +E_{D}\\
           \vspace{0.3cm}
       \textcolor{blue}{ Per v=0, per avere fluorescenza di risonanza si deve avere:}\\
        2E_{R} \lesssim \Gamma \\ \textcolor{black}{(condizione non verificata per nuclei con E_{0}= 100KeV; A=100)}\\
           \end{equation*}
           \vspace{-1.5cm}
        \begin{equation*}

        \textcolor{blue}{Agitazione termica} \Rightarrow \delta v= \sqrt{\frac{k_{B}T}{m}} \Rightarrow \Gamma_{D} = \dfrac{E_{0}\delta v}{c}= \dfrac{E_{0}}{c}\sqrt{\frac{k_{B}T}{m}}\\ \textcolor{black}{(caso tipico nucleare \Gamma_{D}=10^{-3} eV)}  \\     

       \end{equation*}

  \end{frame}

Best Answer

This is a combination of multiple problems:

  • don't leave empty lines in equations

  • put each equation in its own equation* environment

  • don't abuse \\ for line breaks, if you are in text mode, leave an empty line instead

\documentclass{beamer}

\begin{document}

\begin{frame}{Calcolo classico}

    \begin{equation*}
        mv = \dfrac{E_{\gamma}}{c} + m(v-v_{R}); \qquad
        E_{e} + \dfrac{1}{2}mv^{2} = E_{f} + E_{\gamma} + \dfrac{1}{2}m(v-v_{R})^{2}
    \end{equation*}

    \textcolor{blue}{Ponendo:}

    \begin{equation*}         
        E_{R} = \dfrac{1}{2}mv_{R}^{2} = \dfrac{E_{\gamma}^{2}}{2mc^{2}} \approx \dfrac{E_{0}^{2}}{2mc^{2}}; 
    \end{equation*}

    % just the same for the remaining text

\end{frame}

\end{document}
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