  The real Hilbert space formalism developed within the quaternionic quantum
mechanics ($\mathbb H$QM) is fully applied to the simple model of the
autonomous particle. This framework permits novel insights within the usual
description of the complex autonomous particle, particulaly concening the
energy of a non-stationary motion. Through the appraisal of the physical role
played by a fully quaternionic scalar potential, a original self-interaction
within the quaternionic autonomous particle has been determined as well.
Scattering processes are considered to illustrate these novel features.
