Abstract
The Pauli exclusion operator (PEO), which ensures proper symmetry of the eigenstates of multi-electron systems with respect to the exchange of each pair of electrons, is introduced. Once PEO is added to the Hamiltonian, no additional constraints on the multi-electron wave function due to the Pauli exclusion principle are needed. For two-electron states in two dimensions (2D) the PEO can be expressed in a closed form in terms of momentum operators, while in the position representation PEO is a nonlocal operator. Generalizations of PEO for multi-electron systems are introduced. Several approximations to PEO are discussed. Examples of analytical and numerical calculations of PEO are given for the isotropic and anisotropic Hooke's atom in 2D. The application of approximate and kernel forms of PEO for calculations of energies and states in a 2D Hooke's atom are analyzed. The relation of PEO to standard variational calculations with the use of Slater determinant is discussed.
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