The mean-field approximation is a theoretical approach used to simplify complex many-body systems by averaging the effects of all particles on any given particle. This method assumes that each particle experiences an average field generated by the other particles, allowing for a more manageable mathematical treatment of interactions. It plays a crucial role in the Hartree-Fock method and self-consistent field theories, where it helps to account for electron-electron interactions in atoms and molecules without needing to solve the full many-body problem.
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