A method for computing electron momentum densities and Compton profiles from ab initio calculations is presented. This is employed, together with the momentum density spectroscopy known as Compton scattering to investigate the electronic structure of MgCNi3. A method for computing the positron state within a material is also presented. In our method for computing the electron momentum density, reciprocal space is divided into optimally-shaped tetrahedra for interpolation, and the linear tetrahedron method is used to obtain the momentum density and its projections such as Compton profiles. Results are presented and evaluated against experimental data, showing good agreement, and demonstrating the accuracy of our method. For the intermetallic superconductor MgCNi3 , high-resolution x-ray Compton scattering experiments were combined with electronic structure calculations to study a sample with the composition MgCO.93 Ni2.85. Our calculations indicate that the electronic structure, whilst smeared by disorder, does not drastically change in the presence of vacancies, and provide an explanation for some of the discrepancies between measurements of single crystals and polycrystals. Compton scattering measurements were used to determine a Fermi surface in good agreement with that of our supercell calculation, establishing the presence of the hole and electron Fermi surface sheets that are necessary for the proposed two-gap model for the superconductivity. We identify significant smearing of certain parts of the Fermi surface when C and Ni vacancies are present. To calculate the positron state, we have implemented two component density functional theory in the limit of vanishing positron density. We present calculations of the positron lifetime, affinity, and of the momentum density of annihilating electron-positron pairs, for several materials, using a wide variety of electron-positron correlation and enhancement schemes, finding excellent agreement with previous calculations and experimental results. Possible limitations of the method are found in describing positrons localised in vacancies .