Dilation analyticity in constant electric field I. The two body problem. (English) Zbl 0447.47028


47F05 General theory of partial differential operators
47L90 Applications of operator algebras to the sciences
47A55 Perturbation theory of linear operators
81Q15 Perturbation theories for operators and differential equations in quantum theory
Full Text: DOI


[1] Abramowitz, M., Stegun, I.: Handbook of mathematical functions, pp. 448-450. Washington, D.C.: National Bureau of Standards 1964 · Zbl 0171.38503
[2] Agmon, S.: Proceedings of the Tokyo Int. Conf. on Functional Analysis and Related Topics, 1969
[3] Aguilar, J., Combes, J.M.: Commun. math. Phys.22, 269-279 (1971) · Zbl 0219.47011
[4] Apostol, C., Foias, C., Voiculescu, D.: Rev. Roum. Math. Pures Appl.19, 549-577 (1974)
[5] Avron, J., Herbst, I.: Commun. math. Phys.52, 239-254 (1977) · Zbl 0351.47007
[6] Avron, J., Herbst, I., Simon, B.: Phys. Lett.62A, 214-216 (1977)
[7] Avron, J., Herbst, I., Simon, B.: Phys. Rev. Letters39, 1068-1070 (1977)
[8] Avron, J., Herbst, I., Simon, B.: Schrödinger operators with magnetic fields. I. General interactions. Duke Math. J. (to appear) · Zbl 0399.35029
[9] Avron, J., Herbst, I., Simon, J.: Separation of the center of mass in homogeneous magnetic fields (Schrödinger operators with magnetic fields. II). Ann. Phys.114, 431-451 (1978) · Zbl 0409.35027
[10] Avron, J., Herbst, I., Simon, J.: Schrödinger operators with magnetic fields. III. Atoms in magnetic fields. (in preparation) · Zbl 0464.35086
[11] Balslev, E., Combes, J.M.: Commun. math. Phys.22, 280-294 (1971) · Zbl 0219.47005
[12] Brändas, E., Froelich, P.: Phys. Rev. A16, 2207-2210 (1977)
[13] Cerjan, C., Reinhardt, W., Avron, J.: Spectra of atomic Hamiltonians in D.C. fields: Use of the numerical range to investigate the effect of a dilatation transformation. Preprint, University of Colorado 1977
[14] Cerjan, C., Hedges, R., Holt, C., Reinhardt, W., Scheiber, K., Wendoloski, J.: Complex coordinates and the Stark effect. Int. J. Quant. Chem. (to be published)
[15] Combes, J.M., Thomas, L.: Commun. math. Phys.34, 251-270 (1973) · Zbl 0271.35062
[16] Graffi, S., Grecchi, V.: Commun. math. Phys.62, 83-96 (1978)
[17] Herbst, I.: Math. Z.155, 55-70 (1977) · Zbl 0346.47013
[18] Herbst, I., Simon, B.: The Stark effect revisited. Phys. Rev. Letters41, 67-69 (1978)
[19] Herbst, I., Simon, B.: Dilation analyticity in constant electric field. II. TheN-body problem, Borel summability. (in preparation) · Zbl 0473.47038
[20] Herrero, D.: Normal limits of nilpotent operators. Preprint (unpublished) Universidade Esadual de Campinas, Brasil
[21] Howland, J.: Bull. Am. Math. Soc.78, 380-383 (1972) · Zbl 0259.47013
[22] Howland, J.: Pac. J. Math.55, 157-176 (1974)
[23] Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1976 · Zbl 0342.47009
[24] Lavine, R., O’Caroll, M.: J. Math. Phys.18, 1908-1912 (1977)
[25] Nelson, E.: Ann. Math.70, 572-614 (1959) · Zbl 0091.10704
[26] Oppenheimer, J.R.: Phys. Rev.31, 66-81 (1928) · JFM 54.0970.02
[27] Reed, M., Simon, B.: Methods of modern mathematical physics. I, II. New York, London: Academic Press 1972/1973 · Zbl 0242.46001
[28] Reinhardt, W.: Int. J. Quant. Chem. Symp.10, 359-367 (1976)
[29] Riddell, R. C.: Pac. J. Math.23, 377-401 (1967)
[30] Simon, B.: Ann. Math.97, 247-274 (1973) · Zbl 0252.47009
[31] Simon, B.: Phys. Rev. Letters 1145-1146 (1972)
[32] Simon, B.: Resonances and complex scaling: A rigorous overview. Int. J. Quant. Chem. (to appear)
[33] Titchmarsh, E.C.: Eigenfunction expansions associated with second order differential equations. Oxford: Oxford Press 1958 · Zbl 0097.27601
[34] Veseli?, K., Weidmann, J.: Math. Z.156, 93 (1977) · Zbl 0364.35042
[35] Yosida, K.: Functional analysis. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0217.16001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.