Schrödinger equation allows us to write the complete wave equation described by radial an harmonic spherical terms, so, the following work contents are a study of the probability of electron existence in the hydrogen atom, as well the probability of current density resulting as a consequence of these descriptions. Since the wave function can be written in terms of operators the calculation on the relevant operator determined their influence on the particle number which lead to the conclusion that one can write the fields in terms of creation operator and annihilation operator, and this step became known as field quantization (second quantization), the field operator by a certain manner contributes to introducing Feynman's propagator to describe the pair of particle (creation) antiparticle (annihilation) or vice versa.