Bulletin of the American Mathematical Society

Author(s): Barry Simon
Journal: Bull. Amer. Math. Soc. 24 (1991), 303-319.
MSC (1985): Primary 81C12, 81G45, 46C99, 46N05
MathSciNet review: 1066108
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4.: J. Avron and I. Herbst, Spectral and scattering theory of Schrödinger operators related to the Stark effect, Comm. Math. Phys. 52 (1977), 239-254. MR 468862
5.: J. Avron, I. Herbst, and B. Simon, Schrödinger operators with magnetic fields III: Atoms in homogeneous magnetic fields, Comm. Math. Phys. 79 (1981), 529-572. MR 623966
5.: J. Avron, I. Herbst, and B. Simon, The Zeeman effect revisited, Phys. Lett. 62 A (1977), 214-216.
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9.: L. Benassi, V. Grecchi, E. Harrell, and B. Simon, The Bender-Wu formula and the Stark effect in hydrogen, Phys. Rev. Lett. 42 (1979), 704-707.
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13.: R. Damburg, R. Propin, S. Graffi, V. Grecchi, E. Harrell, J. Cizek, J. Palus, and H. Silverstone, 1/R expansion for H2+ : analyticity, summability, asymptotics, and calculation of exponentially small terms, Phys. Rev. Lett. 52(1984), 1112-1115.
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18.: S. Graffi, V. Grecchi, and B. Simon, Borel summability: application to the anharmonic oscillator, Phys. Lett. B32 (1970), 631-634. MR 332068
19.: G. Hardy, Divergent series, Oxford, 1949. MR 30620
20.: J. Hanna, Angle variable holonomy in adiabatic excursion of an integrable Hamiltonian, J. Phys. A18 (1985), 221-230. MR 784910
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22.: E. Harrell, Double wells, Comm. Math. Phys. 75 (1980), 239-261. MR 581948
23.: E. Harrell and B. Simon, The mathematical theory of resonances which have exponentially small widths, Duke Math. J. (1980), 845-902. MR 596118
24.: B. Helffer and J. Sjöstrand, Multiple wells in the semi-classical limit I., Comm. Partial Differential Equations 9 (1984), 337-408. MR 740094
25.: B. Helffer and J. Sjöstrand, Effet tunnel pour l'opérateur de Schrödinger semi-classique. II. résonances, Proc. Nat. Inst. on Micoloral Analysis at "Il Ciocco", Reidel Publ. Co., 1985.
26.: I. Herbst, Dilation analyticity in constant electric field, I. The two-body problem, Comm. Math. Phys. 64 (1979), 279-298. MR 520094
27.: I. Herbst and B. Simon, Some remarkable examples in eigenvalue perturbation theory, Phys. Lett. B78 (1978), 304-306.
28.: I. Herbst and B. Simon, Stark effect revisited, Phys. Rev. Lett. 47 (1978), 67-69. MR 495908
29.: I. Herbst and B. Simon, Dilation analyticity in constant electric field, II. the N-body problem, Borel summability, Comm. Math. Phys. 80 (1981), 181-216. MR 623157
30.: V. Jaksic and J. Segert, Exponential approach to the adiabatic limit, Cal. Tech., preprint.
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32.: T. Kato, Perturbation theory for linear operators, 2nd. ed. Springer-Verlag, Berlin, Heidelberg, New York 1980. (first ed., 1966) MR 203473
33.: J. Loeffel, A. Martin, A. Wightman, and B. Simon, Padé approximants and the anharmonic oscillator, Phys. Lett. B30 (1969), 656-658.
34.: C. Lanczos, Zur Theorie des Starkeffektes in hohen Feldern, Z. für Physik 62 (1931), 204-232.
35.: J. Le Guillou and J. Zinn-Justin, The hydrogen atom in strong magnetic fields: summation of the weak field series expansion, Ann. Phys. 147 (1983), 57.
36.: J. Magnen and R. Sénéor, Phase space cell expansion and Borel summability for the Euclidean φ, Comm. Math. Phys. 56 (1977), 237-276. MR 523030
37.: J. D. Baker, D. E. Freund, R. N. Hill, and J. D. Morgan, III, Radius of convergence and analytic behavior of the 1/Z expansion, Phys. Rev. 41A (1990), 1247-1278. MR 1048862
38.: J. Oppenheimer, Three notes on the quantum theory of aperiodic effects, Phys. Rev. 31 (1928), 66-81.
39.: M. Reed and B. Simon, Methods of modern mathematical physics. IV: analysis of operators, Academic Press, New York, 1978. MR 751959
40.: F. Rellich, Störungstheorie der Spektralzerlegung. I, Math. Ann. 113 (1937), 600-619. MR 1513109
40.: F. Rellich, Störungstheorie der Spektralzerlegung. II, Math. Ann. 113 (1937), 677-685. MR 1513115
40.: F. Rellich, Störungstheorie der Spektralzerlegung. III, Math. Ann. 116 (1939), 555-570. MR 1513244
40.: F. Rellich, Störungstheorie der Spektralzerlegung. IV, Math. Ann. 117 (1940), 356-382. MR 2715
40.: F. Rellich, Störungstheorie der Spektralzerlegung. V, Math. Ann. 118 (1942), 462-484. MR 10791
41.: F. Rellich, Perturbation theory of eigenvalue problems, Gordon & Breach, New York, 1969. MR 240668
42.: E. Schrödinger, Quantisierung als Eigenwertproblem. III, Ann. der Physik 80 (1926), 457-490.
43.: B. Simon, Coupling constant analyticity for the anharmonic oscillator (with an appendix by A. Dicke), Ann. Phys. 58 (1970), 76-136. MR 416322
44.: B. Simon, Quadratic form techniques and the Balslev-Combes theorem, Comm. Math. Phys. 27 (1972), 1-9. MR 321456
45.: B. Simon, Resonances in N-body quantum systems with dilation analytic potentials and the foundations of time dependent perturbation theory, Ann. of Math. (2) 97 (1973), 247-274. MR 353896
46.: B. Simon, Semiclassical analysis of low lying eigenvalues. II. Tunnelling, Ann. of Math. (2) 120 (1984), 89-118. MR 750717
47.: B. Simon, Holonomy, the quantum adiabatic theorem and Berry's phase, Phys. Rev. Lett. 51 (1983), 2167-2170. MR 726866
48.: R. Seznec and J. Zinn-Justin, Summation of divergent series by order dependent mappings: application to the anharmonic oscillator and critical exponents in field theory, J. Math. Phys. 20 (1979), 1398. MR 538715
49.: A. Sokal, An improvement of Watson's theorem on Borel summability, J. Math. Phys. 21 (1980), 261. MR 558468
50.: C. Van Winter, Fredholm equations on a Hilbert space of analytic functions, Trans. Amer. Math. Soc. 162 (1971), 103-139. MR 417849
50.: C. Van Winter, Complex dynamical variables for multiparticle systems with analytic interactions. I, J. Math. Anal. Appl. 47 (1974), 633-670. MR 368663
50.: C. Van Winter, Complex dynamical variables for multiparticle systems with analytic interactions. II, J. Math. Anal. Appl. 48 (1974), 368-399. MR 371308
51.: E. Vock and W. Hunziker, Stability of Schrödinger eigenvalue problems, Comm. Math. Phys. 83 (1982), 281-302. MR 649163
52.: E. Witten, Supersymmetry and Morse theory, J. Differential Geom. 17 (1982), 661-692. MR 683171

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