Two columns and one of them boxed

Question

I would like to place two text (with math expressions) columns and frame one of them, preferably right column; I'm trying to do that with minipage environment but I don't know how to frame it.

MWE:

\documentclass{article}
\usepackage{lipsum}% for macro "\lipsum"
\usepackage{amsmath}% for environment "equation*"
\begin{document}
\noindent
\lipsum[2]

{\vspace{0.5cm}\hfill}
\begin{minipage}[t]{0.45\textwidth}
    \lipsum[1]
    \lipsum[3]
\end{minipage}%
{\hspace*{1cm}}
\begin{minipage}[t]{0.45\textwidth}
    \lipsum[1]
    \begin{equation*}
        \hbar = 2\pi h
    \end{equation*}
    \\
    \lipsum[2]
\end{minipage}%
{\hfill\vspace{0.5cm}}

\noindent
\lipsum[1]
\end{document}

Which produces that

Now I would like to frame right column. Thank you.

Answer 1

Just use \fbox around the box on the right:

\documentclass{article}
\usepackage{lipsum,amsmath}
\begin{document}

\lipsum[2]

\bigskip

\noindent
\begin{minipage}[t]{0.45\textwidth}
    \lipsum[2]
    \lipsum[3]
\end{minipage}\hfill
\fbox{\begin{minipage}[t]{0.45\textwidth}
    \lipsum*[2]
    \begin{equation*}
        \hbar = 2\pi h
    \end{equation*}
    \lipsum[2]
\end{minipage}}

\bigskip

\lipsum[1]
\end{document}

Note that {\vspace{0.5}\hfill} makes little sense; better using something like \bigskip. Also there's no point in doing {\hspace{1cm}} (the outer braces are useless, by the way) when \hfill will do.

Answer 2

This is an answer for the question in version 1 and 2. Version 3 might be solved using \fbox{...} around the minipage. But the details (horizontal/vertical spacing, support for page breaks, ...) elude me.

Two columns, the right column is framed:

\documentclass{article}
\begin{document}
  \begin{tabular}{l|l|}
    \cline{2-2}
    abc & def \\
    $\displaystyle\sum_{i=1}^n f(n)$ & $\displaystyle\frac{\pi}{4} e^{-\sin\alpha}$ \\
    mno & pqr \\
    \cline{2-2}
  \end{tabular}
\end{document}