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We extend our previous work on symplectic semiclassical Gaussian wave packetdynamics to incorporate electromagnetic interactions by including a vectorpotential. The main advantage of our formulation is that the equations ofmotion derived are naturally Hamiltonian. We obtain an asymptotic expansion ofour equations in terms of $\hbar$ and show that our equations have$\mathcal{O}(\hbar)$ corrections to those presented by Zhou, whereas ours alsorecover the equations of Zhou in the case of a linear vector potential andquadratic scalar potential. One and two dimensional examples of a particle in amagnetic field are given and numerical solutions are presented and comparedwith the classical solutions and the expectation values of the correspondingobservables as calculated by the Egorov or Initial Value Representation (IVR)method. We numerically demonstrate that the $\mathcal{O}(\hbar)$ correctionterms improve the accuracy of the classical or Zhou's equations for short timesin the sense that our solutions converge to the expectation values calculatedusing the Egorov/IVR method faster than the classical solutions or those ofZhou as $\hbar \to 0$.

Hamiltonian Dynamics of Semiclassical Gaussian Wave Packets in Electromagnetic Potentials