The Penning trap is the workhorse of laboratory equipment for conducting high-precision measurements and yet its theoretical description suffers from a dichotomy. One uses either the classical description based on the concept of trajectories or the quantum description based on the concept of wave functions. At first glance, these two modes of description may appear mutually exclusive. However, I will demonstrate that they can be unified into a single framework, with classical trajectories embedded into wave functions. The centers of the resulting wave packets move exactly like classical particles and their shapes do not change.