2025/06/17 by N. Q. San, O. D. Skoromnik, San, N. Q. +5
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2506.14661
openalex publication_date 2025/06/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
In our work we construct a Hamiltonian, whose eigenstates approximate the solutions of the self-consistent Hartree-Fock equations for nonrelativistic atoms and ions. Its eigenvalues are given by completely algebraic expressions and the eigenfunctions are defined by Coulomb wave-functions orbitals. Within this approximation we compute the binding energy, ionization potentials, electron density distribution, electron density at the nucleus, and atomic scattering factors of nonrelativistic atoms and ions. The accuracy of our results is comparable with those obtained via the usage of the Hartree-Fock method but does not require solving integro-differential equations or numerically computing integrals with complex functions. This approach can serve as a good initial approximation for performing more accurate calculations and for the quantitative evaluation of physical parameters that depend on the electron density of atoms. The proposed approach is of interest for various fields of condensed matter physics, plasma physics and quantum chemistry.