Angular-momentum quantization applied to the Thomas-Fermi atom

The Fermi momentum of an electron in a statistical atom can be considered as a vector sum of two components. The first represents the orbital movement of an electron and can be calculated from the quantum levels of the angular momentum. The second is the maximum progressive momentum of the same electron and can be obtained from the variational procedure given by Gombas. A new expression for the Fermi momentum leads to the modification of the Thomas-Fermi statistical equation given by Barnes and Cowan.