Making equation fit on one beamer slide

Question

I'm doing a presentation and one of the slides has a particularly long equation, which I want to fit on the page. What's the best way to fit this on the page without altering the size of the other text slides? Thanks in advance.

\documentclass{beamer}
\usetheme{metropolis}
\begin{document}
\begin{frame}
\frametitle{Equation}
\begin{align}\label{global_energy_slab_sl_1}
    &|\mathcal{\hat R}|^2+|\mathcal{\hat T}|^2 = \frac{1+|\hat V|^2}{|\hat H|^2} \\ \nonumber
    &= \frac{1+(r_{0}^{+}r_{1}^{-}e^{i\lambda_{1}^{-}L}+r_{0}^{-}r_{1}^{+}e^{i\lambda_{1}^{+}L})(r_{0}^{+}r_{1}^{-}e^{-i\lambda_{1}^{-}L}+r_{0}^{-}r_{1}^{+}e^{-i\lambda_{1}^{+}L})}{(r_{0}^{-}r_{1}^{-}e^{i\lambda_{1}^{-}L}+r_{0}^{+}r_{1}^{+}e^{i\lambda_{1}^{+}L})(r_{0}^{-}r_{1}^{-}e^{-i\lambda_{1}^{-}L}+r_{0}^{+}r_{1}^{+}e^{-i\lambda_{1}^{+}L})} \\ \nonumber
    &=\frac{1+(r_{0}^{+})^2(r_{1}^{-})^2+(r_{0}^{-})^2(r_{1}^{+})^2+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{2i\zeta_1 L}+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{-2i\zeta_{1} L}}{(r_{0}^{-})^2(r_{1}^{-})^2+(r_{0}^{+})^2(r_{1}^{+})^2+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{2i\zeta_1 L}+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{-2i\zeta_{1} L}},
\end{align}
\end{frame}
\end{document}

Answer 1

I would simply use, for the longest fractions, the medium-size fractions from nccmath (they're about 80 % of \displaystyle size):

\documentclass{beamer}
\usetheme{metropolis}
\usepackage{nccmath}
\begin{document}

\begin{frame}
\frametitle{Equation}
\begin{align}\label{global_energy_slab_sl_1}
    &|\mathcal{\hat R}|^2+|\mathcal{\hat T}|^2 = \frac{1+|\hat V|^2}{|\hat H|^2} \\ \nonumber
    &= \mfrac{1+(r_{0}^{+}r_{1}^{-}e^{i\lambda_{1}^{-}L}+r_{0}^{-}r_{1}^{+}e^{i\lambda_{1}^{+}L})(r_{0}^{+}r_{1}^{-}e^{-i\lambda_{1}^{-}L}+r_{0}^{-}r_{1}^{+}e^{-i\lambda_{1}^{+}L})}{(r_{0}^{-}r_{1}^{-}e^{i\lambda_{1}^{-}L}+r_{0}^{+}r_{1}^{+}e^{i\lambda_{1}^{+}L})(r_{0}^{-}r_{1}^{-}e^{-i\lambda_{1}^{-}L}+r_{0}^{+}r_{1}^{+}e^{-i\lambda_{1}^{+}L})} \\[1ex] \nonumber
   & =\mfrac{1+(r_{0}^{+})^2(r_{1}^{-})^2+(r_{0}^{-})^2(r_{1}^{+})^2+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{2i\zeta_1 L}+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{-2i\zeta_{1} L}}{(r_{0}^{-})^2(r_{1}^{-})^2+(r_{0}^{+})^2(r_{1}^{+})^2+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{2i\zeta_1 L}+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{-2i\zeta_{1} L}}
\end{align}
\end{frame}

\end{document} 

Answer 2

If you want to keep your slide content verbatim, you could place your environment in a group and insert some font size instruction (such as \tiny) in that group. Because it would be inside the group, the size change would be limited to the grouped elements.

\documentclass{beamer}
\usetheme{metropolis}
\begin{document}
\begin{frame}
\frametitle{Equation}
{\tiny % or \scriptsize, \footnotesize, \small, etc.
\begin{align}\label{global_energy_slab_sl_1}
    &|\mathcal{\hat R}|^2+|\mathcal{\hat T}|^2 = \frac{1+|\hat V|^2}{|\hat H|^2} \\ \nonumber
    &= \frac{1+(r_{0}^{+}r_{1}^{-}e^{i\lambda_{1}^{-}L}+r_{0}^{-}r_{1}^{+}e^{i\lambda_{1}^{+}L})(r_{0}^{+}r_{1}^{-}e^{-i\lambda_{1}^{-}L}+r_{0}^{-}r_{1}^{+}e^{-i\lambda_{1}^{+}L})}{(r_{0}^{-}r_{1}^{-}e^{i\lambda_{1}^{-}L}+r_{0}^{+}r_{1}^{+}e^{i\lambda_{1}^{+}L})(r_{0}^{-}r_{1}^{-}e^{-i\lambda_{1}^{-}L}+r_{0}^{+}r_{1}^{+}e^{-i\lambda_{1}^{+}L})} \\ \nonumber
    &=\frac{1+(r_{0}^{+})^2(r_{1}^{-})^2+(r_{0}^{-})^2(r_{1}^{+})^2+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{2i\zeta_1 L}+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{-2i\zeta_{1} L}}{(r_{0}^{-})^2(r_{1}^{-})^2+(r_{0}^{+})^2(r_{1}^{+})^2+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{2i\zeta_1 L}+(r_{0}^{-}r_{0}^{+})(r_{1}^{-}r_{1}^{+})e^{-2i\zeta_{1} L}},
\end{align}}
\end{frame}
\end{document}

If you were willing to be more flexible, you could perhaps omit the offending expression from your equality and at your presentation you could remark something to the effect of "after some tedious distribution of the terms in 109 we can use this identity in 110 to acquire this result in 111."