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arXiv · 2101.03445

The Pauli Exclusion Operator: example of Hooke's atom

Tomasz M. Rusin·Wlodek Zawadzki
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Abstract

The Pauli Exclusion Operator (PEO) which ensures proper symmetry of the eigenstates of multi-electron systems with respect to exchange of each pair of electrons is introduced. Once PEO is added to the Hamiltonian, no additional constraints on 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 non-local operator. Generalizations of PEO for multi-electron systems is introduced. Several approximations to PEO are discussed. Examples of analytical and numerical calculations of PEO are given for isotropic and anisotropic Hooke's atom in~$2D$. Application of approximate and kernel forms of PEO for calculations of energies and states in~$2D$ Hooke's atom are analyzed. Relation of PEO to standard variational calculations with the use of Slater determinant is discussed.

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Tomasz M. Rusin, Wlodek Zawadzki. 2021-01-09. The Pauli Exclusion Operator: example of Hooke's atom. https://doi.org/10.1103/physreva.103.052221

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