Weyl Representation of the Permutation Operators and Exchange Interaction

摘要

Weyl phase-space representation is derived for the cyclic permutation operators that naturally occur in the quantum theory of exchange interaction.The classical-like phase-space representation of exchange leads to a special type of coupling between the position and momentum variables.With Gaussian electronic structure basis sets in mind,it is shown that the position-momentum coupling seen in the Weyl representation of the exchange interaction is best described by diffuse Gaussians.A classical phase-space analog of exchange is derived for the Heisenberg-Dirac spin-Hamiltonian.Novel one-elec tron Wigner functions are introduced for description of the two-electron spin correlations.