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On Green's functions, propagators, and sturmians for the nonrelativistic coulomb problem
Author(s) -
Blinder S. M.
Publication year - 1984
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560260828
Subject(s) - propagator , semiclassical physics , physics , coulomb , coulomb wave function , eigenvalues and eigenvectors , quantum mechanics , feynman diagram , mathematical physics , quantum , electron
Recent progress in the mathematical physics and quantum chemistry of Coulomb Green's functions is summarized. Analogy with the defining relation for the Green's function has led to a finite model for the Fermi contact interaction which avoids spurious divergences in second‐order perturbation calculations. The Hamilton‐Jacobi mechanics of the Coulomb problem is reviewed. A compact parametrization for Hamilton's principal and characteristic functions provides a key element in further developments. These include a semiclassical representation for the Coulomb propagator in Feynman's formalism and a new propagator in the domain of Coulomb Sturmian eigenstates. In projected applications, approximate many‐electron Green's functions constructed from combinations of one‐particle Coulomb propagators provide a basis for computation of atomic and molecular eigenvalue spectra.