In the present work, we have analyzed the motion of a structured matter wave in the presence of a constant magnetic field under the influence of a time-dependent external force. We have introduced exact propagator kernels obtained from partial differential equations based on the Heisenberg equations of motion. The initial wave function is assumed to be a Gauss–Hermite wave function. For the evolved wave function, we have obtained and discussed the uncertainties, orbital angular momentum and the inertia tensor in the center of mass frame of the density function. From the quantum interferometry of matter waves point of view, and also non-relativistic quantum electron microscopy, the results obtained here are important and more reliable than approximate methods like the axial approximation.
