While driving up from Wales to London, I realised that the tabular was redundant for the question as asked, and when I arrived, I found that @Caramdir had justly taken me to task. Here is a completely new answer, which addresses a bit more than the original question.
For a single line of text, all you need to do is align the node:
\begin{tikzpicture}
\node at (0,0) (a) {a};
\node at (5,5) (b) {b};
\node[draw=black,inner sep=2mm,thick,rectangle,fit=(a) (b)] (x) {};
\node[anchor=south east,inner sep=1pt] at (x.south east)
{$ H \Psi = \nabla \Psi $};
\end{tikzpicture}
For multiple lines, things get a bit more elephantine, though the next release of Tikz will have, I believe, constructs like align=right for text. Meanwhile, one way is to use a tabular:
\begin{tikzpicture}
\node at (0,0) (a) {a};
\node at (5,5) (b) {b};
\node[draw=black,inner sep=0pt,thick,rectangle,fit=(a) (b)] (x) {};
\node[anchor=south east] at (x.south east) {%
\begin{tabular}{r}
$ H \Psi = \nabla \Psi $\\
$ J \Phi = \nabla \Phi $
\end{tabular}
};
\end{tikzpicture}
You may want to tweak the tabular parameters to alter the space between the right/bottom of the text
and the corner of the rectangle...