Because the Heisenberg Hamiltonian presumes the electrons involved in the exchange coupling are localized in the context of the Heitler–London, or valence bond (VB), theory of chemical bonding, it is an adequate model for explaining the magnetic properties of electrically insulating narrow-band ionic and covalent non-molecular solids where this picture of the bonding is reasonable.
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The effective potential includes the external potential and the effects of the Coulomb interactions between the electrons, e.g., the exchange and correlation interactions.
This interaction Hamiltonian includes direct Coulomb interaction energy and exchange interaction energy between electrons.