Regular sized fonts in oubraces package

Just use \dfrac instead of \frac

If you like, you could add some \rules for increasing the vertical spacing.

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{oubraces}

\begin{document}
Without \verb|\rule|:
\begin{equation}
\overunderbraces{&&\br{1}{\text{Diagonal in $k$-space}}&&\br{3}{\text{Diagonal in $x$-space}}}{i\hbar\dfrac{d\psi_n(x)}{dt}&=&-\dfrac{\hbar^2}{2m}\dfrac{\partial^2\psi_n(x)}{\partial x^2}&+&\dfrac{1}{2}m\omega^2x^2\psi_n(x)&+&f(x,t)\psi_n(x)}{&&\br{3}{\text{Diagonal in Hermite-Gauss basis}}&&\br{1}{\text{Diagonal in $x$-space}}}
\end{equation}
With \verb|\rule|:
\begin{equation}
\overunderbraces{&&\br{1}{\text{Diagonal in $k$-space}}&&\br{3}{\text{Diagonal in $x$-space}}}{i\hbar\dfrac{d\psi_n(x)}{dt}&=&\rule[-10pt]{0pt}{30pt}-\dfrac{\hbar^2}{2m}\dfrac{\partial^2\psi_n(x)}{\partial x^2}&+&\dfrac{1}{2}m\omega^2x^2\psi_n(x)&+&f(x,t)\psi_n(x)}{&&\br{3}{\text{\rule{0pt}{7pt}Diagonal in Hermite-Gauss basis}}&&\br{1}{\text{Diagonal in $x$-space}}}
\end{equation}

\end{document}

You can patch \overunderbraces to use \displaystyle for the main formula when in a display environment (equation, align and so on), checking for \if@display that's provided by amsmath.

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{oubraces}
\usepackage{etoolbox}

\makeatletter
\patchcmd{\overunderbraces}
  {&\hfil$}
  {&\hfil$\if@display\displaystyle\fi}
  {}{}
\patchcmd{\overunderbraces}
  {&\hfil${}}
  {&\hfil$\if@display\displaystyle\fi{}}
  {}{}
\makeatother


\begin{document}

\begin{equation}
\overunderbraces{%
  &&\br{1}{\text{Diagonal in $k$-space}}%
  &&\br{3}{\text{Diagonal in $x$-space}}%
}{%
  i\hbar\frac{d\psi_n(x)}{dt}%
  &=%
  &-\frac{\hbar^2}{2m}\frac{\partial^2\psi_n(x)}{\partial x^2}%
  &+%
  &\frac{1}{2}m\omega^2x^2\psi_n(x)
  &+
  &f(x,t)\psi_n(x)%
}{%
  &&\br{3}{\text{Diagonal in Hermite-Gauss basis}}%
  &&\br{1}{\text{Diagonal in $x$-space}}%
}
\end{equation}

\end{document}

Note that I used {-} after the & in order to fix the spacing.