  Let a reductive group $G$ act on a smooth affine complex algebraic variety
$X.$ Let $\mathfrak{g}$ be the Lie algebra of $G$ and $\mu:T^*(X)\to
\mathfrak{g}$ be the moment map. If the moment map is flat, and for a generic
character $\chi:\mathfrak{g}\to\mathbb{C}$, the action of $G$ on
$\mu^{-1}(\chi)$ is free, then we show that for very generic characters $\chi$
the corresponding quantum Hamiltonian reduction of the ring of differential
operators $D(X)$ is simple.
