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Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. V: Lower bounds and path integrals. (English) Zbl 0464.35085


MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
81U10 \(n\)-body potential quantum scattering theory
81T99 Quantum field theory; related classical field theories
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[1] Agmon, S.: On exponential decay of solutions of second order elliptic equation in unbounded domains. Proc. A. Pleijel Conf., Uppsala, September 1979 (in preparation)
[2] Agmon, S.: Private communication
[3] Ahlrichs, R.: J. Math. Phys. (NY)14, 1860-1863 (1973)
[4] Ahlrichs, R., Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T.: Phys. Rev. A18, 328 (1978)
[5] Ahlrichs, R., Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T., Morgan III, J.: Phys. Rev. A (to appear)
[6] Aizenman, M., Simon, B.: Brownian motion and Harnack’s inequality for Schrödinger operators (in preparation) · Zbl 0459.60069
[7] Auberson, G., Mahoux, G., Menessier, G.: Nuovo Cimento A48, 1-23 (1978)
[8] Azencott, R.: Larges déviations et applications. Ecole d’eté de probabilitiés de Saint Flour VIII. 1978, Hennequin, P.L. (ed.) Lecture notes in mathematics, Vol. 774, pp. 1-176 (1980)
[9] Bardos, C., Merigot, M.: Proc. R. Soc. Edinburgh76, 323-344 (1977)
[10] Brascamp, H., Lieb, E.H., Luttinger, J.M.: J. Funct. Anal.17, 227-237 (1974) · Zbl 0286.26005
[11] Brezin, E., Le Guillou, J.C., Zinn-Justin, J.: Phys. Rev. D15, 1544-1557 (1977)
[12] Carmona, R.: Commun. Math. Phys.62, 97-106 (1978) · Zbl 0403.47016
[13] Carmona, R.: J. Funct. Anal.33, 259-296 (1979) · Zbl 0419.60075
[14] Collins, J.C., Soper, D.E.: Ann. Phys.112, 209 (1978)
[15] Combes, J.M., Thomas, L.: Commun. Math. Phys.34, 251-276 (1973) · Zbl 0271.35062
[16] Deift, P.: Private communication
[17] Deift, P., Hunziker, W., Simon, B., Vock, E.: Commun. Math. Phys.64, 1-34 (1978) · Zbl 0419.35079
[18] Donsker, M., Varadhan, S.R.S.: Commun. Pure Appl. Math.28, 1-47, 279-301 (1975);29, 389-461 (1976) · Zbl 0323.60069
[19] Faris, W.G.: Bull. Am. Math. Soc. (New Series)2, 522-530 (1980)
[20] Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. London, New York: Academic Press 1970 · Zbl 1042.35002
[21] Goldstein, H.: Classical mechanics. London, Amsterdam, Paris: Addison-Wesley 1950 · Zbl 0043.18001
[22] Herbst, I., Sloan, A.: Trans. Am. Math. Soc.236, 325-360 (1978)
[23] Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T.: Phys. Rev.16A, 1782-1785 (1977)
[24] Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T., Ahlrichs, R., Morgan III, J.: On the exponential falloff of wave functions and electron densities. Mathematical problems in theoretical physics. Proceedings. Lausanne 1979. Osterwalder, K. (ed.). Lecture notes in physics, Vol. 116, pp. 62-67 (1980) · Zbl 0446.35017
[25] Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T., Simon, B.: J. Phys. A13, 1131-1133 (1980)
[26] Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T., Simon, B.: Proc. Am. Math. Soc. (to appear)
[27] Hoffmann-Ostenhof, T.: J. Phys. A13, 417-424 (1980)
[28] Hoffmann-Ostenhof, T.: Phys. Lett.77A, 140 (1980)
[29] Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0148.12601
[30] Kovalenko, V., Semenov, Yu.: Russ. Math. Surv.33, 119-157 (1978) · Zbl 0413.47011
[31] Landau, L.D., Lifschitz, E.M.: Mechanics. Oxford, New York: Pergamon Press 1960
[32] Lieb, E.H., Simon, B.: Adv. Appl. Math. (to appear)
[33] Lipatov, L.N.: Sov. Phys. JETP25, 104-107 (1977)
[34] Lithner, L.: Ark. för Mat. Astron. Pys.5, 281-285 (1964)
[35] Meyer, P.A.: La formule de Ito pour le mouvement Brownien d’après Brosamler. Séminaire de probabilités XII. In Lecture notes in math., Vol. 649, pp. 763-769 (1978)
[36] McKean, H.P.: Stochastic integrals. London, New York: Academic Press 1969 · Zbl 0191.46603
[37] Mercuriev, S.: Sov. J. Nucl. Phys.19, 222-229 (1974)
[38] Mol?anov, S.A.: Russ. Math. Surv.30, 1-63 (1975) · Zbl 0315.53026
[39] Morgan III, J.: J. Phys. A10, L91-L93 (1977)
[40] O’Connor, T.: Commun. Math. Phys.32, 319-340 (1973)
[41] Pincus, M.: Trans. Am. Math. Soc.134, 193-216 (1968)
[42] Reed, M., Simon, B.: Methods of modern mathematical physics. I. Functional analysis. (2nd Ed.). London, New York: Academic Press 1981 · Zbl 0459.46001
[43] Reed, M., Simon, B.: Methods of modern mathematical physics. IV. Analysis of operators. London, New York: Academic Press 1978 · Zbl 0401.47001
[44] Schilder, M.: Trans. Am. Math. Soc.125, 63-85 (1965)
[45] Sigal, I., Sigalov, A.G.: Theor. Math. Phys. (USSR)5, 990-1005 (1970)
[46] Simon, B.: Proc. Am. Math. Soc.42, 395-401 (1974)
[47] Simon, B.: Proc. Am. Math. Soc.45, 454-456 (1974)
[48] Simon, B.: Trans. Am. Math. Soc.208, 317-329 (1975)
[49] Simon, B.: Functional integration and quantum physics. London, New York: Academic Press 1979 · Zbl 0434.28013
[50] Simon, J. Funct. Anal.35, 215-229 (1980) · Zbl 0446.47041
[51] Slaggie, E.L., Wichmann, E.H.: J. Math. Phys. (NY)3, 946-968 (1962)
[52] Spencer, T.: Private communication
[53] Spivak, M.: A comprehensive introduction to differential geometry, Vol. I (2nd ed.). Berkeley Publish or Perish 1979 · Zbl 0439.53003
[54] Truddinger, N.S.: Ann. Scuol. Norm. Sup. Pisa27, 265-308 (1973)
[55] Varadhan, S.R.S.: Commun. Pure Appl. Math.20, 659-685 (1967) · Zbl 0278.60051
[56] Ventcel, A.D.: Theor. Probab. Its Appl. (USSR)17, 515-517 (1972)
[57] Ventcel, A.D.: Theor. Probab. Its Appl. (USSR)21, 227-242, 499-512 (1976) · Zbl 0361.60005
[58] Ventcel, A.D., Freidlin, M.I.: Russ. Math. Surv.25, 1-55, (1970) · Zbl 0297.34053
[59] Ventcel, A.D., Freidlin, M.I.: Theor. Probab. Its Appl. (USSR)17, 269-283 (1972)
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