Resolutions of the Coulomb operator
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We discuss a generalization of the resolution of the identity by considering one-body resolutions of two-body operators, with particular emphasis on the Coulomb operator. We introduce a set of functions that are orthonormal with respect to 1 r12 and propose that the resulting "resolution of the Coulomb operator," r12 -1 = ? fi > < fi ?, may be useful for the treatment of large systems due to the separation of two-body interactions. We validate our approach by using it to compute the Coulomb energy of large systems of point charges. © 2008 American Institute of Physics.
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