Resolutions of the Coulomb operator
MetadataShow full item record
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.
Showing items related by title, author, creator and subject.
Practical application of failure criteria in determining safe mud weight windows in drilling operationsGholami, Raoof; Moradzadeh, A.; Rasouli, V.; Hanachi, J. (2014)Wellbore instability is reported frequently as one of the most significant incidents during drilling operations. Analysis of wellbore instability includes estimation of formation mechanical properties and the state of in ...
Determination of safe mud window considering time-dependent variations of temperature and pore pressure: Analytical and numerical approachesRezagholilou, Ali; Behnoud far, P.; Vialle, Stephanie; Madadi, Mahyar (2017)Wellbore stability is a key to have a successful drilling operation. Induced stresses are the main factors affecting wellbore instability and associated problems in drilling operations. These stresses are significantly ...
Kadyrov, Alisher; Bray, Igor; Mukhamedzhanov, A.; Stelbovics, Andris (2009)We formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both ...