A II-1 Non-Relativistic Hamiltonian Trajectories AII-2 Relativistic Hamiltonian Trajectories $\left\{\begin{array}{l}\frac{\text{d}r}{\text{d}t}=\frac{\partial H}{\partial p}\equiv \frac{p}{m}\\ \frac{\text{d}p}{\text{d}t}=-\frac{\partial H}{\partial r}\equiv -\nabla \left[V\left(r\right)+W\left(r,E\right)\right]\\ \nabla \cdot \left({R}^{2}p\right)=0\\ |p\left(t=0\right)|\equiv {p}_{0}=\sqrt{2mE}\end{array}$ $\left\{\begin{array}{l}\frac{\text{d}r}{\text{d}t}=\frac{\partial H}{\partial p}\equiv \frac{{c}^{2}p}{E-V\left(r\right)}\\ \frac{\text{d}p}{\text{d}t}=-\frac{\partial H}{\partial r}\equiv -\nabla V\left(r\right)-\frac{E}{E-V\left(r\right)}\nabla W\left(r,E\right)\\ \nabla \cdot \left({R}^{2}p\right)=0\\ |p\left(t=0\right)|\equiv {p}_{0}=\sqrt{{\left(E/c\right)}^{2}-{\left({m}_{0}c\right)}^{2}}\end{array}$ $W\left(r,E\right)=-\frac{{\hslash }^{2}}{2m}\frac{{\nabla }^{2}R\left(r,E\right)}{R\left(r,E\right)}$ $W\left(r,E\right)=-\frac{{\hslash }^{2}{c}^{2}}{2E}\frac{{\nabla }^{2}R\left(r,E\right)}{R\left(r,E\right)}$