Quaternionic quantum particles: new solutions

If $\mathrm{\Psi }$ is a quaternionic wave function, then $i\mathrm{\Psi }\mathrm{\ne }\mathrm{\Psi }i$. Thus, there are two versions of the quaternionic Schr"odinger equation (QSE). In this article, we present the second possibility for solving the QSE, following on from a previous article. After developing the general methodology, we present the quaternionic free particle solution and the scattering of the quaternionic particle through a scalar barrier.