  We compute the degree of the generalized Pl\"ucker embedding $\kappa$ of a
Quot scheme $X$ over $\PP^1$. The space $X$ can also be considered as a
compactification of the space of algebraic maps of a fixed degree from $\PP^1$
to the Grassmanian $\rm{Grass}(m,n)$. Then the degree of the embedded variety
$\kappa (X)$ can be interpreted as an intersection product of pullbacks of
cohomology classes from $\rm{Grass}(m,n)$ through the map $\psi$ that evaluates
a map from $\PP^1$ at a point $x\in \PP^1$. We show that our formula for the
degree verifies the formula for these intersection products predicted by
physicists through Quantum cohomology~\cite{va92}~\cite{in91}~\cite{wi94}. We
arrive at the degree by proving a version of the classical Pieri's formula on
the variety $X$, using a cell decomposition of a space that lies in between $X$
and $\kappa (X)$.
