  In the present work, we have analyzed the motion of a structured matter wave
in the presence of a constant magnetic field and 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 as 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 point of view of the quantum
interferometry of matter waves, and also non-relativistic quantum electron
microscopy, the results obtained here are important and more reliable than the
approximate methods like the axial approximation.
