On the Extended Hilbert Space in the theory of the multielectron atom

The construction of the Extended Hilbert Space (EHS) is presented in the form of a direct sum of the spaces of vectors of finite and infinite norms as the main space in the mathematical formalism of quantum mechanics of a multielectron atom. On the example of constructing the analytical structure of the probability amplitude 1s - 3p of photoexcitation of a neon atom, the implementation of the EHS - construct for solving the equations of the self-consistent Hartree-Fock field is given.