Trace formula for Schrödinger operator with Coulomb potential in three-dimensional space
Teoretičeskaâ i matematičeskaâ fizika, Tome 70 (1987) no. 1, pp. 104-114 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Schrodinger operator in $R^3$ with a potential which is equal to the sum of the Coulomb part and a fast decreasing part is considered. Trace formulas of zeroth order are found for this operator. These formulas connect the determinant of a regularized scattering operator at zero energy with the characteristics of the discrete spectrum.
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     author = {A. A. Kvitsinskiy},
     title = {Trace formula for {Schr\"odinger} operator with {Coulomb} potential in three-dimensional space},
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A. A. Kvitsinskiy. Trace formula for Schrödinger operator with Coulomb potential in three-dimensional space. Teoretičeskaâ i matematičeskaâ fizika, Tome 70 (1987) no. 1, pp. 104-114. http://geodesic.mathdoc.fr/item/TMF_1987_70_1_a7/

[1] Buslaev V. S., Faddeev L. D., DAN SSSR, 132:1 (1960), 13–16 | MR | Zbl

[2] Buslaev V. S., DAN SSSR, 143:5 (1962), 1067–1070 ; Проблемы математической физики, Т. 1, ЛГУ, Л., 1966, 82–101 | MR | Zbl | MR

[3] Levinson N., Mat-fys. meld. Kgl. danske Vid. selskab., 25 (1949), 9 | MR | Zbl

[4] Bollé D., Osborn T. A., Phys. Rev. A, 26:6 (1982), 3062–3072 | DOI | MR

[5] Seaton M. J., Compt. rend., 240 (1955), 1317; Яфаев Д. Р., ТМФ, 11:1 (1972), 78–92 | MR

[6] Kvitsinskii A. A., TMF, 68:2 (1986), 244–254 | MR

[7] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, T. 4, Mir, M., 1982 | MR

[8] Birman M. Sh., Krein M. G., DAN SSSR, 144:3 (1962), 475–478 | MR | Zbl

[9] Dollard J., J. Math. Phys., 5 (1964), 729 | DOI | MR

[10] Hostler R., J. Math. Phys., 8 (1967), 642 | DOI

[11] Kvitsinskii A. A., Komarov I. V., Merkurev S. P., YaF, 38:1 (1983), 101–114

[12] Merkurev S. P., Faddeev L. D., Kvantovaya teoriya rasseyaniya v sistemakh neskolkikh chastits, Nauka, M., 1985 | MR

[13] Titchmarsh E., Teoriya funktsii, Nauka, M., 1980 | MR | Zbl