×

Double wells. (English) Zbl 0445.35036


MSC:

35J10 Schrödinger operator, Schrödinger equation
35P15 Estimates of eigenvalues in context of PDEs
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
81T99 Quantum field theory; related classical field theories
Full Text: DOI

References:

[1] Coleman, S.: The uses of instantons. In: Proceedings of the International School of Physics, Erice, Italy, 1977 (to appear)
[2] Harrell, E.M.: Commun. Math. Phys.60, 73-95 (1978) · Zbl 0395.34023 · doi:10.1007/BF01609474
[3] Br?zin, E., Parisi, G., Zinn-Justin, J.: Phys. Rev. D16, 408-412 (1977)
[4] Isaacson, D.: Comm. Pure App. Math.29, 531-551 (1976) · doi:10.1002/cpa.3160290506
[5] Fr?man, N., Fr?man, P.-O.: JWKB approximation, contribution to the theory. Amsterdam: North-Holland, 1965;
[6] Fr?man, N.: Ark. Fys.31, 445-451 (1966);
[7] Fr?man, N., Fr?man, P.-O., Myhrman, U., Paulsson, R.: Ann. Phys.74, 314-323 (1972) · doi:10.1016/0003-4916(72)90143-1
[8] Kac, M.: Mathematical mechanisms of phase transitions. In: Brandeis Univ. Summer Institute in Theoretical Physics, 1966, Vol. 1. (eds. M. Chr?tien, E.P. Gross, S. Desai). New York: Gordon and Breach 1968
[9] Ashkin, J., Lamb, W.E., Jr.: Phys. Rev.64, 159-178 (1943) · doi:10.1103/PhysRev.64.159
[10] Newell, G.F., Montroll, E.W.: Rev. Mod. Phys.25, 353-389 (1953) · Zbl 0053.18601 · doi:10.1103/RevModPhys.25.353
[11] Thompson, C.J., Kac, M.: Studies Appl. Math.48, 257-264 (1969)
[12] Condon, E.U., Shortley, G.H.: The theory of atomic spectra. Cambridge: Cambridge University Press 1970 · Zbl 0117.23805
[13] Herring, C.: Rev. Mod. Phys.34, 631-645 (1962) · Zbl 0109.22805 · doi:10.1103/RevModPhys.34.631
[14] Jacobi, C.G.J.: Vorlesungen ?ber Dynamik. Berlin: G. Reiner 1884 · JFM 16.0028.01
[15] Thirring, W.: Course in mathematical physics, Vol. I. Classical dynamical systems. New York, Vienna: Springer 1978 · Zbl 0387.70001
[16] Pauli, W.: Ann. Phys.68, 177-240 (1922) · doi:10.1002/andp.19223731102
[17] Jaff?, G.: Z. Phys.87, 535-544 (1934) · doi:10.1007/BF01333263
[18] Bates, D.R., Ledsham, K., Stewart, A.L.: Phil. Trans. Roy. Soc. London A246, 215-240 (1953)
[19] Damburg, R.J., Propin, R.Kh.: J. Phys. B, Ser. 2,1, 681-691 (1968) · doi:10.1088/0022-3700/1/4/319
[20] Thirring, W.: Lehrbuch der mathematischen Physik, Vol. III. Quantenmechanik von Atomen und Molek?len. Vienna: Springer 1979. English translation to appear 1980 · Zbl 0408.46054
[21] Aventini, P., Seiler, R.: Commun. Math. Phys.41, 119-134 (1975) · doi:10.1007/BF01608753
[22] Combes, J.-M., Seiler, R.: Internat. J. Quantum Chem.14, 213-229 (1978) · doi:10.1002/qua.560140209
[23] Morgan J.D., III, Simon, B.: Behavior of molecular potential envergy curves for large nuclear separations (to appear)
[24] Reed, M., Simon, B.: Methods of modern mathematical physics, in four volumes. New York: Academic Press 1972, 1975, 1979, 1978 · Zbl 0242.46001
[25] Temple, G.: Proc. Roy. Soc. London119A, 276-293 (1928)
[26] Kato, T.: J. Phys. Soc. Japan4, 334-339 (1949) · doi:10.1143/JPSJ.4.334
[27] Harrell, E.M.: Proc. Am. Math. Soc.69, 271-276 (1978)
[28] Harrell, E.M.: Ann. Phys.119, 351-369 (1979) · Zbl 0412.34013 · doi:10.1016/0003-4916(79)90191-X
[29] Slaggie, E.L., Wichmann, E.H.: J. Math. Phys.3, 946-968 (1962) · doi:10.1063/1.1724311
[30] Glazman: I.M.: Direct methods of qualitative spectral analysis of singular differential operators. Jerusalem: Israel Program for Scientific Translation 1965 · Zbl 0143.36505
[31] Bardos, C., M?rigot, M.: Comptes Rendues Acad. Sci. Paris281A, 561-563 (1975)
[32] Deift, P., Hunziker, W., Simon, B., Vock, E.: Comm. Math. Phys.64, 1-34 (1978) · Zbl 0419.35079 · doi:10.1007/BF01940758
[33] Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T.: Phys. Rev. A16, 1782-1785 (1977)
[34] Kato, T.: Commun. on Pure and Appl. Math.10, 151-177 (1957) · Zbl 0077.20904 · doi:10.1002/cpa.3160100201
[35] Abramowitz, M., Stegun, I. (eds.): Handbook of mathematical functions. NBS Applied Mathematics Series 55. Washington: National Bureau of Standards 1964 · Zbl 0171.38503
[36] Klaus, M., Simon, B.: Ann. Inst. Henri Poincar?30, 83-87 (1979)
[37] Schiff, L.I.: Quantum mechanics, 3rd ed. New York: McGraw-Hill 1968 · Zbl 0068.40202
[38] Simon, B.: Ann. Phys.58, 76-136 (1970) · doi:10.1016/0003-4916(70)90240-X
[39] Hsieh, P.-F., Sibuya, Y.: J. Math. Anal. Appl.16, 84-103 (1966) · Zbl 0161.05803 · doi:10.1016/0022-247X(66)90188-0
[40] Lubkin, G.B.: Physics Today32, No. 5, 17-19 (1979)
[41] Flammer, C.: Spheroidal wave functions. Stanford, California: Stanford University Press 1957 · Zbl 0078.05703
[42] Buchholz, H.: The confluent hypergeometric function. Berlin, Heidelberg, New York: Springer 1969 · Zbl 0169.08501
[43] Herbst, I., Sloan, A.: Trans. Am. Math. Soc.236, 325-360 (1978)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.