# N-body equations

These types are used to represent the integro-differential equations that result from the variation of the energy expression with respect to an orbital. They can, in general, be written on the form

$$$$$0 = \Omega_1\ket{\chi}\braket{a}{b}...$$$$$

when varying with respect to a conjugated orbital, and

$$$$$0 = \bra{\chi}\Omega_1\braket{a}{b}...$$$$$

when varying with respect to an orbital. In both cases, $\Omega_1$ is a one-body operator, either in itself, or resulting from a contraction over all coordinates but one of a many-body operator (see ContractedOperator).

EnergyExpressions.NBodyEquationType
NBodyEquation{N,O}(orbital, operator::NBodyOperator[, factor::NBodyTerm])

Equation for an orbital, acted upon by an operator, which may be a single-particle operator, or an N-body operator, contracted over all coordinates but one, and optionally multiplied by an NBodyTerm, corresponding to overlaps/matrix elements between other orbitals.

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