In Physics the energy of any system represents a sensitive variable because of it depends the functionality and evolution of system at time. Thus the deep knowledge of the interactions of system might be a remarkable advantage as to anticipate stochastic fluctuations as well as minimize the errors at the done measurements. Thus, in this paper a particular attention is paid on the mathematical characteristics of the quantum mechanics evolution operator when it is projected onto a full scenario of principles based at Machine Learning. In concrete the case of pass of charged particle through a bunch of charged particles can be perceived as a system exhibiting oscillations because the attraction and repulsion forces experienced along the space-time trajectory. The fact that the energy can be controllable by using free parameters can be advantageous in the sense of providing a learning to the system in order to optimize the total energy at key space-time coordinates.