  We solve the largest sample eigenvalue distribution problem in the rank 1
spiked model of the quaternionic Wishart ensemble, which is the first case of a
statistical generalization of the Laguerre symplectic ensemble (LSE) on the
soft edge. We observe a phase change phenomenon similar to that in the complex
case, and prove that the new distribution at the phase change point is the GOE
Tracy--Widom distribution.
