I will conduct a series of numerical calculations relating to the one-electron addition and removal spectral function of the one dimensional Hubbard model. This work uses novel first principle expressions for said spectral function, emanating from Carmelo's "Pseudofermion Dynamical Theory" (PDT) which describes the quantum objects diagonalising the normal ordered Hubbard hamiltonian. This theory, based on Takahashi's string hypothesis, utilises spin-charge separation of the electron's degrees of freedom, to produce energy eigenfunctions factorisable into a charge and a spin function, respectively. This factorisation was previously studied in great detail in the infinite on-site repulsion limit, but is now, thanks to the framework offered by the PDT, also extended to arbitrary values of the on-site Coloumb repulsion. The calculation depends on expressions that live in a 5D, and a 6D, parameter space, respectively, neccesitating the usage of powerful computation resources to enable fruitful results planned to be published during 2025 if all goes well.