Semiclassical eigenvalues for non-separable bound systems from classical trajectories: The degenerate case

References

• Chapman , S. , Garrett , B.C. and Miller , W.H. 1976 . J. chem. Phys. , 64 : 502 – 502 .
   Web of Science ®Google Scholar
• Percival , I.C. and Pomphrey , N. 1976 . Molec. Phys. , 31 : 97 – 97 .
   Web of Science ®Google Scholar
• Marcus , R.A. 1973 . Faraday Discuss. chem. Soc. , 34 – 34 . Molecular Beam Scattering . 55
   Google Scholar
• Eastes , W. and Marcus , R.A. 1974 . J. chem. Phys. , 61 : 4301 – 4301 .
   Web of Science ®Google Scholar
• Noid , D.W. and Marcus , R.A. 1975 . J. chem. Phys. , 62 : 2119 – 2119 .
   Web of Science ®Google Scholar
• Sorbie K.S. Molec. Phys. in press 1976
   Google Scholar
• Percival I.C. Adv. chem. Phys. in press 1976 This gives a review of semiclassical bound state theory with an account of the invariant toroids of classical mechanics, EBK quantization, etc.
   Google Scholar
• Percivial , I.C. 1974 . J. Phys. A , 7 : 794 – 794 .
   Google Scholar
• Einstein , A. 1917 . Verh. dt. phys. Ges. , 19 : 82 – 82 .
   Google Scholar
• Brillouin , M.L. 1926 . J. Phys., Paris , 7 : 353 – 353 .
   Google Scholar
• Keller , J.B. 1958 . Ann. Phys. (N. Y.) , 4 : 180 – 180 .
   Web of Science ®Google Scholar
• Sharman , R.V. 1963 . Vibrations and Waves , Butterworths .
   Google Scholar
• Percival , I.C. 1973 . J. Phys. B , 6 : L229 – L229 .
   Web of Science ®Google Scholar
• Henon , M. and Heiles , C. 1964 . Astr. J., N.Y. , 69 : 73 – 73 .
   Web of Science ®Google Scholar
• Born , M. 1924 . Mechanics of the Atom , Ungar & Co. . 1960
   Google Scholar
• Walker , G.H. and Ford , J. 1969 . Phys. Rev. , 188 : 416 – 416 .
   Web of Science ®Google Scholar
• Wintner , A. 1947 . The Analytical Foundations of Celestial Mechanics , Princeton University Press .
   Google Scholar
• Contopoulos , G. 1963 . Astr. J., N.Y. , 68 : 763 – 763 .
   Web of Science ®Google Scholar
• Poincaré , H. 1897 . New Methods of Celestial Mechanics Vol. III , (translated by NASA, document N67-27279).
   Google Scholar
• Kolmogorov , A.N. 1967 . “ English translation of appropriate work in Appendix D of Abraham, R. ” . In Foundations of Mechanics , W. A. Benjamin .
   Google Scholar
• Arnol'd , V.I. 1963 . Russ. math. Surveys , 18 : 9 – 9 . and 85 (translated from Russian)
   Google Scholar
• Moser , J. 1962 . Nach. Akad. Wiss. Göttingen , 1 : 1 – 1 .
   Google Scholar
• Contopoulos , G. 1963 . Astrophys. J. , 138 : 1297 – 1297 . 1970, Astr. J., N.Y., 75, 96; 1971, Ibid., 76, 147.
   Web of Science ®Google Scholar
• Barbanis , B. 1966 . Astr. J., N.Y. , 71 : 415 – 415 .
   Web of Science ®Google Scholar
• Mo , K.C. 1972 . Physica , 57 : 445 – 445 .
   Google Scholar
• Contopoulos , G. and Moutsoulas , M. 1965 . Astr. J., N.Y. , 70 : 817 – 817 .
   Web of Science ®Google Scholar
• Thom , R. 1975 . Structural Stability and Morphogenesis , Benjamin . This explains the topological basis of catastrophe theory and gives several applications.
   Google Scholar
• Zeeman , E.C. 1976 . Scient. Am. , 234 ( 4 ) : 65 – 65 . A general layman's review of catastrophe theory with several applications mainly to the behavioural sciences.
   Web of Science ®Google Scholar
• Berry , M.V. 1976 . Adv. Phys. , 25 : 1 – 1 .
   Web of Science ®Google Scholar
• See, for example, figure 3 (c) in Berry M.V. Adv. Phys. 1976 25 1 1
   Web of Science ®Google Scholar
• Golstein , H. 1950 . Classical Mechanics , Addison-Wesley .
   Google Scholar
• Nordholm , S. and Rice , S.A. 1974 . J. chem. Phys. , 61 : 203 – 203 . and 768
   Web of Science ®Google Scholar
• Mayers , D.F. 1962 . Numerical Solution of Ordinary and Partial Differential Equations , Edited by: Fox , L. Pergmon . The NAG routine DO2AAF was used in this calculation
   Google Scholar
• Froberg , C.E. 1965 . Introduction to Numerical Analysis , Addison-Wesley .
   Google Scholar
• Handy , N.C. , Colwell , S.M. and Miller , W.H. 1976 . Faraday Discuss. chem. Soc. ,
   Google Scholar
• Sorbie , K.S. 1976 . unpublished work
   Google Scholar
• Gutzwiller , M.C. 1967 . J. math. Phys. , 8 : 1979 – 1979 . 1969, Ibid., 10, 1004; 1970, Ibid., 11, 1791; 1971, Ibid., 12, 343.
   Web of Science ®Google Scholar