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 λ1(M) of the Laplacian, which is λ1(M) ≤ (2n + 1)2. If the equality holds, then either M has
only one end, or M is diffeomorphic to R × N with N given by a compact manifold. Moreover, if M is of bounded curvature,
M is covered by the quaterionic hyperbolic space QHn and N is a compact quotient of the generalized Heisenberg group. When
λ1(M) ≥ 8(n+2) 3 , we also prove that M must have only one end with infinite volume.