Laboratory experiments on the electrochemical remediation of the environment. Part 9: Microscale recovery of a soil metal pollutant and its extractant

Abstract

In this paper, the Feynman path integral technique is applied for superintegrable potentials on two-dimensional spaces of nonconstant curvature: these spaces are Darboux spaces D I and D II. On D I, there are three, and on D II four such potentials. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is either determined by a transcendental equation involving parabolic cylinder functions (Darboux space I), or by a higher order polynomial equation. The solutions on D I in particular show that superintegrable systems are not necessarily degenerate. We can also show how the limiting cases of flat space (constant curvature zero) and the two-dimensional hyperboloid (constant negative curvature) emerge. " Nauka/Interperiodica 2007.",,,,,,"10.1134/S1063779607030021",,,"http://hdl.handle.net/20.500.12104/43498","http://www.scopus.com/inward/record.url?eid=2-s2.0-34249935224&partnerID=40&md5=6657156137b432dc4fcf0095c04de515",,,,,,"3",,"Physics of Particles and Nuclei",,"299

325",,"38",,"Scopus

WOS",,,,,,,,,,,,"Path integral approach for superintegrable potentials on spaces of nonconstant curvature: I. Darboux spaces D I and D II",,"Article" "44249","123456789/35008",,"Ibanez, J.G., Centro Mexicano de Quimica Verde y Microescala, Departamento de Ingenieria y Ciencias Quimicas, Universidad Iberoamericana, Prol. Reforma 880, 01219 Mexico, D. F., Mexico; Balderas-Hernandez, P., Facultad de Quimica, Centro Conjunto de Investigacion en Quimica Sustentable UAEM-UNAM, Universidad Autonoma Del Estado de Mexico, Carretera Toluca-Atlacomulco, Km 14.5, Toluca, Estado de Mexico, Mexico; García-Pintor, E., Centro Mexicano de Quimica Verde y Microescala, Departamento de Ingenieria y Ciencias Quimicas, Universidad Iberoamericana, Prol. Reforma 880, 01219 Mexico, D. F., Mexico; Barba-Gonzalez, S.N., Departamento de Quimica, CUCEI, Universidad de Guadalajara, Boulevard Marcelino García Barragan #1451, 44430 Guadalajara, Mexico; Doria-Serrano, M.D.C., Centro Mexicano de Quimica Verde y Microescala, Departamento de Ingenieria y Ciencias Quimicas, Universidad Iberoamericana, Prol. Reforma 880, 01219 Mexico, D. F., Mexico; Hernaiz-Arce, L., Centro Mexicano de Quimica Verde y Microescala, Departamento de Ingenieria y Ciencias Quimicas, Universidad Iberoamericana, Prol. Reforma 880, 01219 Mexico, D. F., Mexico; Diaz-Perez, A., Centro Mexicano de Quimica Verde y Microescala, Departamento de Ingenieria y Ciencias Quimicas, Universidad Iberoamericana, Prol. Reforma 880, 01219 Mexico, D. F., Mexico; Lozano-Cusi, A., Centro Mexicano de Quimica Verde y Microescala, Departamento de Ingenieria y Ciencias Quimicas, Universidad Iberoamericana, Prol. Reforma 880, 01219 Mexico, D. F., Mexico",,"Ibanez, J.G.

Balderas-Hernandez, P.

García-Pintor, E.

Barba-Gonzalez, S.N.

Doria-Serrano, M.D.C.

Hernaiz-Arce, L.

Diaz-Perez, A.

Lozano-Cusi, A.",,"2011",,"Many soils throughout the world are contaminated with metal salts of diverse toxicity. We have developed an experiment to demonstrate the removal of a metal froman insoluble surrogate soil pollutant, CuCO3 · Cu(OH)2, by complexation followed by the simultaneous electrochemical recovery of the ligand (i.e., EDTA) and of the metal in its elemental form (i.e., Cu0). We have calculated speciation diagrams to predict appropriate conditions and to interpret the results. Copyright " 2011 American Chemical Society and Division of Chemical Education, Inc.