The operator approach for representing the symmetry of many-electron systems (series I)

This work reports on a new and effective method that simplifies the many-electron problem. Instead of a wave function, an operator is used to describe the symmetry of the many-electron system through a transformation. It is proven that the two approaches are physically equivalent, but the operator formalism works much more effectively than the wave function formalism. In the operator formalism, the wave function of an n-electron system can be separated into its spatial and spin parts, and the symmetries of identical particles can be correctly described. For example, it can provide the correct spin and spatial symmetry of many-electron atoms or molecules. For many-electron atoms, one can obtain the simultaneous eigenfunction of L̂2 and Ŝ2. Consequently, the spectroscopic terms of a configuration can be obtained, for example, the hydrogen atom in an energy formula with four quantum numbers (n, l, ml, and ms) for each electron in an atom, including the Hartree–Fock theory. We theoretically analyze and discuss the atomic structure of many-electron atoms using this formula.