Geodesic
Analytic properties of solution of electronic Schrödinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 1, pp. 31-36 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that for a nondegenerate electronic state of a molecule the energy is an analytic function of the nuclear coordinates everywhere except points at which the nuclei coincide. The proof is based on construction of a parametric substitution of the coordinates and an associated analytic family of operators. It is found that the eigenfunctions of the molecular Hamiltonian do not have a square integrable third derivative with respect to the nuclear coordinates. 
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     author = {P. V. Ganelin and V. I. Pupyshev},
     title = {Analytic properties of solution of electronic {Schr\"odinger} equation},
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P. V. Ganelin; V. I. Pupyshev. Analytic properties of solution of electronic Schrödinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 1, pp. 31-36. http://geodesic.mathdoc.fr/item/TMF_1991_88_1_a5/

[1] Maslov V. P., Asimptoticheskie metody i teoriya vozmuschenii, Nauka, M., 1988 | MR

[2] Kato T., Trans. Amer. Math. Soc., 70:2 (1951), 195–211 | DOI | MR | Zbl

[3] Kato T., Comm. Pure and Appl. Math., 10:2 (1957), 151–177 | DOI | MR | Zbl

[4] Zhislin G. M., DAN SSSR, 128 (1959), 231–234 | MR | Zbl

[5] Cycon H., Froese R. G., Kirsch W., Simon B., Schrödinger Operators, Springer Verlag, Berlin–Heidelberg–New York, 1987 | MR | Zbl

[6] Berezin F. A., Shubin M. A., Uravnenie Shredingera, MGU, M., 1983 | MR

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

[8] Mnogoelektronnaya zadacha v kvantovoi khimii, Naukova dumka, Kiev, 1987, S. 7–21

[9] Aventini P., Seller R., Commun. Math. Phys., 41:2 (1975), 119–134 | DOI | MR

[10] Combes J. M., Seller R., Int. J. Quantum. Chem., 14:2 (1978), 213–229 | DOI

[11] Hagedorn J. A., Commun. Math. Phys., 117:3 (1988), 387–404 | DOI | MR

[12] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[13] Shabat B. V., Vvedenie v kompleksnyi analiz, T. 2, Nauka, M., 1985 | MR

[14] Berry M. V., Proc. Roy. Soc., A392:1802 (1984), 45–47 | DOI | MR

[15] Iorgens K., Vaidmann I., Spektralnye svoistva gamiltonovykh operatorov, Mir, M., 1976 | MR

[16] Hanziker W., Ann. Inst. H. Poincare, A45:4 (1986), 339–358