Abstract
Theories of semiclassical bound state spectra for systems with N freedoms are reviewed, emphasizing the different features occurring on successively finer scales of energy E, measured in terms of h, and attempting to correlate these with whether the underlying classical motion is regular or irregular.
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References
Noid, D.W., and Marcus, R.A.: 1977, J. Chem. Phys. 67, pp. 559–567.
Eastes, W., and Marcus, R.A.: 1974, J. Chem. Phys. 61, pp. 4301–4306.
Noid, D.W., and Marcus, R.A.: 1975, J. Chem. Phys. 62, pp. 2119–2124.
Noid, D.W., Koszykowski and Marcus, R.A.: 1979, J. Chem. Phys. 71, pp. 2864–2873.
Percival, I.C., and Pomphrey, N.: 1976, Mol. Phys. 31, pp. 97–114.
Jaffe, C, and Reinhardt, W.P.: 1979, J. Chem. Phys. 71, pp. 1862–1869.
Chapman, S., Garrett, B., and Miller, W.H.: 1976, J. Chem. Phys. 64, pp. 502–509.
Ford, J.: 1975,in ‘Fundamental Problems in Statistical Mechanics’ (ed. E.G.D. Cohen) Vol. 111, pp. 215–255. North-Holland.
Arnol’d, V.I., ‘Mathematical Methods of Classical Dynamics’, (Springer, New York 1978).
Berry, M.V.: 1978, in ‘Topics in Nonlinear Dynamics’ (ed. S. Jorna), Am. Inst. Phys. Conf. Proc. 46, pp. 16–120.
Helleman, R.: 1980, in’ Fundamental Problems in Statistical Mechanics (ed. E.G.D. Cohen), Vol. V, pp. 165–233, North-Holland.
Berry, M.V.: 1981,’ semiclassical Mechanics of Regular and Irregular Motion’, Les Houches Summer School Lectures, to be published by North-Holland).
Gutzwiller, M.C.: 1967, J. Math. Phys. 8, pp. 1979–2000.
Gutzwiller, M.C.: 1969, J. Math. Phys. 10, pp. 1004–1020.
Gutzwiller, M.C.: 1970, J. Math. Phys. 11, pp. 1791–1806.
Gutzwiller, M.C.: 1971, J. Math. Phys., 12, pp. 343–358.
Gutzwiller, M.C.: 1978, in ‘Path Integrals and their Application in Quantum, Statistical and Solid State Physics’ (eds.: G.J. Papadopoulos and J.T. Devreese), pp. 163–200, Plenum, N.Y.
Balian, R., and Bloch, C.: 1970, Ann. Phys. N.Y. 60, pp. 401–447.
Balian, R., and Bloch, C.: 1971, Ann. Phys. N.Y. 64, pp. 271–307.
Balian, R., and Bloch, C.: 1972, Ann. Phys. N.Y. 69, pp. 76–160.
Balian, R., and Bloch, C.: 1974, Ann. Phys. N.Y. 85, pp. 514–545.
Landau, L.D., and Lifshitz, E.M.: 1965, in ‘Quantum Mechanics (Nonrelativistic Theory)’ (Oxford: Pergamon)
Berry, M.V., and Mount, K.E.: 1972, Reps. Prog. Phys. 35, pp. 315–397.
Baltes, H.P., and Hilf, E.R. 1978, ‘Spectra of Finite Systems’ (B-I Wissenschaftsverlag, Mannheim).
Marcus, R.A.: 1980, in ‘Nonlinear Dynamics’, Ann. N.Y. Acad. Sci. 357, pp.169–182 (ed. R.H.G. Helleman).
Berry, M.V.: 1981, Ann. Phys. N.Y. 131, pp. 163–216.
Sinai, Ya. G.: 1970, Russ. Math. Surv. 25 No. 2, pp. 137–189.
Bunimovich, L.A.: 1974, Funct. Anal. Appl. 8, pp. 254–255, 1979, Commun. Math. Phys. 65, pp. 295–312.
Berry, M.V., and Tabor, M.: 1976, Proc. Roy. Soc. A349, pp. 101–123.
Berry, M.V., and Tabor, M.: 1977, J. Phys. A.10, pp. 371–379.
Rajaraman, R.: 1975, Phys. Rept. 21, pp. 227–313.
DeWitt, C, Maheshwari, A., and Nelson, B.: 1979, Phys. Rept. 50, pp. 255–372.
Miller, W.H.: 1975, J. Chem. Phys. 63, pp. 996–999.
Voros, A.: 1976, Annls. Inst. H. Poincare XXIV, pp. 31–90.
Gutzwiller, M.C.: 1980, Phys. Rev. Lett. 45, pp. 150–153.
Chazarain, J.: 1974, Inv. Math. 24, pp. 65–82.
Einstein, A.: 1917, Ver. Deut. Phys. Ges. 19, pp. 82–92.
Keller, J.B.: 1958, Ann. Phys. N.Y. 4, pp. 180–188.
Maslov, V.P., and Fedoriuk, M.V., in ‘Semi-classical approximation in quantum mechanics’ (D. Reidel: Dordrecht 1981) (original Russian edition 1965).
Percival, I.C.: 1977, Advan. Chem. Phys. 36, pp. 1–61.
Percival, I.C.: 1973, J. Phys. B6, pp. L229–232.
Porter, C.F. (ed.): 1965, in ‘Statistical Theory of Spectra: Fluctuations’ (Academic Press, N.Y. 1965).
McDonald, S.W., and Kaufman, A.N.: 1979, Phys. Rev. Lett. 42, pp. 1189–1191.
Casati, G., Valz-Gris, F., and Guarneri, I.: 1980, Nuovo Cimento Lett. 28, pp. 279–282.
Berry, M.V., and Tabor, M.: 1977, Proc. Roy. Soc. A356, pp. 375–394.
Richens, P.J., and Berry, M.V.: 1981, Physica 2D, pp. 495–512.
Neumann, J. von, and Wigner, E.P.: 1929, Physik, Z.30, pp. 467–470.
Teller, E.: 1937, J. Phys. Chem. 41, pp. 109–116.
Pechukas, P.: 1972, J. Chem. Phys. 57, pp. 5577–5594.
Uhlenbeck, K.: 1976, Amer. J. Math. 98, pp. 1059–1078.
Pokrovskii, V.L.: 1966, JETP Lett. 4, pp. 96–99.
Noid, D.W., Koszykowski, M.L., Tabor, M., and Marcus, R.A.: 1980, J. Chem. Phys. 72, pp. 6169–75.
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Berry, M.V. (1984). Structures in Semiclassical Spectra: A Question of Scale. In: Diner, S., Fargue, D., Lochak, G., Selleri, F. (eds) The Wave-Particle Dualism. Fundamental Theories of Physics, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6286-6_12
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DOI: https://doi.org/10.1007/978-94-009-6286-6_12
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