The application of Thomas - Fermi method to calculate the electron spectrum in highly doped n-Si quantum wires is presented under finite temperatures, where the many-body effects, like exchange, are taken into account. The electron potential energy is calculated from a single equation. Then the electron energy sub-levels and wave functions within the potential well are simulated from the Schrödinger equation. For axially symmetric wave functions the shooting method has been used. Two methods have been applied to solve the Schrödinger equation in the case of the anisotropic effective mass, the variation method and the iteration procedure for the eigenvectors of the Hamiltonian matrix
