  Let $M^{4n}$ be a complete quaternionic K\"ahler manifold with scalar
curvature bounded below by $-16n(n+2)$. We get a sharp estimate for the first
eigenvalue $\lambda_1(M)$ of the Laplacian which is $\lambda_1(M)\le (2n+1)^2$.
If the equality holds, then either $M$ has only one end, or $M$ is
diffeomorphic to $\mathbb{R}\times N$ with N given by a compact manifold.
Moreover, if $M$ is of bounded curvature, $M$ is covered by the quaterionic
hyperbolic space $\mathbb{QH}^n$ and $N$ is a compact quotient of the
generalized Heisenberg group. When $\lambda_1(M)\ge \frac{8(n+2)}3$, we also
prove that $M$ must have only one end with infinite volume.
