In this paper, we have given the general solution for the eigen functions of I in term for non-relativistic wave functions. Consequently, we have tried to derive spinor representations as well as spin and current densities for the energy eigen states of the various integrals of motion. In the paper, we have ignored the anti-field which come into existence when a magnetic field is applied. How much these anti-fields, which are a direct product of the fields, are going to affect the construction of energy eigen functions, are not calculated. Different relations for spin density and matter current are also assumed. The Lorentz transformation to accelerate the system could be fitted in, but with difficulties because of various constraints. Since, distance plays pivotal role in the activities of anti-fields, the rebound positions and values take an anti-form vis a vis uniform magnetic fields. This further complicate the problem because each of these is to be replaced by its transpose.