The Time-Dependent Hartree-Fock Formalism of the Double Excited States of the Helium Atom

Abstract:

The solution of the time-dependent Schrödinger equation for the helium atom in double excited states using the time-dependent Hartree-Fock (TDHF) equation is outlined in this work. Schwartz interpolation is used to derive grid representations that are particularly suitable for problems involving the Coulomb potential. This method allows a non-uniform spatial discretization of grid and provides an accurate description of the excited states, eigenvalues and wave functions with a few numbers of grid points. We have introduced the solution using the Coulomb Wave Function Discrete Variable Representation (CWDVR) which is an economical and promising step towards a more efficient treatment of many-electron systems. The equation is transformed into a diffusion type equation by an imaginary-time evolution method and the solution is obtained numerically. The asymptotic solution of these equations leads to definite energy double excited states. We have shown that the calculated electronic energies for the helium atom agree well with the best available values.

• Periodical: Key Engineering Materials (Volume 1029)
• Pages: 3-10
• DOI: https://doi.org/10.4028/p-U5uTHQ
• Online since: November 2025
• Authors: Dagviikhorol Naranchimeg, Sukh Ochir, Gonchigsuren Munkhsaikhan*
• Keywords: Cardinal Function, Grid Points, Imaginary Time, Interpolation, Self-Consistent Field

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