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Path Integral Discussion for Smorodinsky-Winternitz Potentials: I.\ Two- and Three Dimensional Euclidean Space
Path integral formulations for the Smorodinsky-Winternitz potentials in two-
and three-dimen\-sional Euclidean space are presented. We mention all
coordinate systems which separate the Smorodinsky-Winternitz potentials and
state the corresponding path integral formulations. Whereas in many coordinate
systems an explicit path integral formulation is not possible, we list in all
soluble cases the path integral evaluations explicitly in terms of the
propagators and the spectral expansions into the wave-functions.Comment: LaTeX 60 pages, DESY 94-01
Challenges to Path Integral Formulations of Quantum Theories
The functional integral has many triumphs in elucidating quantum theory. But
incorporating charge fractionalization into that formalism remains a challenge.Comment: 8 pages, 5 figure
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Localized boundary-domain integral formulations for problems with variable coefficients
Specially constructed localized parametrixes are used in this paper instead of a fundamental solution to reduce a boundary value problem with variable coefficients to a localized boundary-domain integral or integro-differential equation (LBDIE or LBDIDE). After discretization, this results in a sparsely populated system of linear algebraic equations, which can be solved by well-known efficient methods. This make the method competitive with the finite element method for such problems. Some methods of the parametrix localization are discussed and the corresponding LBDIEs and LBDIDEs are introduced. Both mesh-based and meshless algorithms for the localized equations discretization are described
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