  We study the elastic scattering of quantum particles based on a real Hilbert
space approach to quaternionic quantum mechanics ($\mathbbm H$QM) and derive
expression for the wave function, the phase shifts, as well as the optical
theorem for the case of a hard sphere scattering potential. The strong
agreement between these new quaternionic results and the corresponding results
in complex quantum mechanics reinforce the validity of the $\mathbbm H$QM
generalization of ordinary complex quantum mechanics ($\mathbbm C$QM).
