Numerical Investigation on the Thomas–Fermi Model and Its Quantum and Exchange Corrections

The Thomas–Fermi model and its quantum and exchange corrections with mathematic manipulations and numerical approaches are primarily investigated. The reduced ideal electron chemical potential is adopted as the initial value for the iterative solution of the Thomas–Fermi model. A new transformation for the quantum and exchange equations is proposed to apply the boundary conditions easily. Both the Thomas–Fermi equation and correction equations are solved with the Runge–Kutta algorithm. The mathematical difficulties in controlling the computing accuracy of the equations containing the Fermi–Dirac integral are settled. The equation of state, based on the Thomas–Fermi model with its quantum and exchange corrections, is constructed and compared with relevant data.