A Numerical Method for Solving the Time Dependent Hartree-Fock Equations of the Helium Atom

This paper presents an efficient and accurate method for solving the time-dependent Hartree-Fock equations for the helium atom in the ground and single excited states. The radial coordinate is discretized by the discrete variable representation (DVR), which is constructed from Coulomb wave functions. To solve the equation, the spectral method with Coloumb wave functions is used as a basis. We illustrate that the calculated electronic energies for the helium atom are in good agreement with the best available experimental values. The CWDVR method proves to be more economical and efficient as it uses the optimal few numbers of grid points compared to other numerical calculations.