Outro Revisado por pares

Semiclassical theory of Bound States

1977; Wiley; Linguagem: Inglês

10.1002/9780470142554.ch1

ISSN

1934-4791

Autores

I C Percival,

Tópico(s)

Laser-Matter Interactions and Applications

Resumo

Semiclassical theory of Bound States Ian C. Percival, Ian C. Percival Department of Applied Mathematics, Queen Mary College, Mile End Road, London, E1 4NS EnglandSearch for more papers by this author Ian C. Percival, Ian C. Percival Department of Applied Mathematics, Queen Mary College, Mile End Road, London, E1 4NS EnglandSearch for more papers by this author Book Editor(s):I. Prigogine, I. Prigogine University of Brussels, Brussels, Belgium and University of Texas Austin, TexasSearch for more papers by this authorStuart A. Rice, Stuart A. Rice University of Texas, Austin, Texas and Department of Chemistry, The James Franck Institute, The University of Chicago, Chicago, IllinoisSearch for more papers by this author First published: 01 January 1977 https://doi.org/10.1002/9780470142554.ch1Citations: 421Book Series:Advances in Chemical Physics AboutPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShareShare a linkShare onEmailFacebookTwitterLinkedInRedditWechat Summary This chapter contains sections titled: Introduction and early theories Classical mechanics for one degree of freedom Semiclassical mechanics for one degree of freedom Classical mechanics for many degrees of freedom; Polyatomic molecules and invariant toroids Semiclassical mechanics for many degrees of freedom Practical EBK quantization Regular and irregular spectra Classical trajectories References A. Einstein, Verhand. Deut. Phys. Ges., 19, 82 (1917). Google Scholar M. V. Berry and K. E. Mount, Reports Progr. Phys., 35, 315 (1972); 10.1088/0034-4885/35/1/306 CASWeb of Science®Google Scholar R. A. Marcus, J. Chem. Phys., 56, 311 (1972); 10.1063/1.1676866 CASWeb of Science®Google Scholar H. Kreek, R. L. Ellis, and R. A. Marcus, J. Chem. Phys., 61, 4540 (1974); 10.1063/1.1681771 CASWeb of Science®Google Scholar W. H. Miller, Advan. Chem. Phys, 25, 69 (1974); 10.1002/9780470143773.ch2 Google Scholar Advan. Chem. Phys, 30, 77 (1975); 10.1002/9780470143827.ch3 CASGoogle Scholar M. S. Child, Molec. Phys., 29, 1421 (1975); 10.1080/00268977500101241 CASWeb of Science®Google Scholar J. N. L. Connor, Ann. Rept. Progr. Chem. A, 70, 5 (1973); CASWeb of Science®Google Scholar Molec. Phys., 31, 33 (1976); 10.1080/00268977600100041 CASWeb of Science®Google Scholar J. J. Duistermaat, Commun. Pure Appl. Math., 27, 207 (1974). 10.1002/cpa.3160270205 Web of Science®Google Scholar See Ref. 2. For early work see Ref. 12 of R. Balian and C. Bloch, Ann. Phys. (N. Y.) 85, 514 (1974). 10.1016/0003-4916(74)90421-7 Web of Science®Google Scholar G. Starkschall and J. C. Light, J. Chem. Phys., 61, 3417 (1974) and references therein. 10.1063/1.1682508 CASWeb of Science®Google Scholar J. L. Dunham, Phys. Rev., 41, 721 (1932); 10.1103/PhysRev.41.721 CASWeb of Science®Google Scholar P. N. Argyres, Physics 2, 131 (1965); 10.1103/PhysicsPhysiqueFizika.2.131 Google Scholar N. Fröman and P. O. Fröman, Ann. Phys. (N. Y.) 83, 103 (1974). 10.1016/0003-4916(74)90379-0 Web of Science®Google Scholar See Ref. 2. Google Scholar K. Schwarzschild, Berliner Berichte, 548 (1916); Google Scholar P. S. Epstein, Ann. der Physik, 50, 489 (1916). 10.1002/andp.19163551302 CASGoogle Scholar M. Jammer, Conceptual Developments of Quantum Mechanics, McGraw-Hill, New York, 1966 Chapters 2 and 3. Web of Science®Google Scholar M. L. Brillouin, J. de Physique (Ser. 6) 7, 353 (1926); 10.1051/jphysrad:01926007012035300 Google Scholar J. B. Keller, Ann. Phys. (N. Y.) 4, 180 (1958). 10.1016/0003-4916(58)90032-0 Web of Science®Google Scholar V. Maslov, Theorie des Perturbations, Dunod, Paris, 1972. Google Scholar Our Maslov index function σq is related to the Maslov index Ind[l(A, B)] of Ref. 10 by σq(B)−σq(A)=2Ind[l(A,B)] The factor 2 is introduced to ensure that σp, like σq, is an integer. The term Maslov index in this chapter refers to the index α for closed trajectories on toroids only, in which case it has the same meaning as in Ref. 10. Google Scholar H. G. Goldstein, Classical Mechanics, Addison-Wesley, Reading, Mass., 1953; Google Scholar H. C. Corben and P. Stehle, Classical Mechanics, Wiley, New York, 1950. Web of Science®Google Scholar L. Landau and E. M. Lifshitz, Mechanics, Pergamon, Oxford, 1960. Google Scholar M. Born, Mechanics of the Atom, Ungar, New York, 1960, Chapter 2. Google Scholar D. W. Noid and R. A. Marcus, J. Chem. Phys., 62, 2119 (1975). 10.1063/1.430777 CASWeb of Science®Google Scholar Y. Hagihara, Celestial Mechanics, MIT Press, Cambridge, Mass., 1970. Google Scholar W. Eastes and R. A. Marcus, J. Chem. Phys., 61, 4301 (1974). 10.1063/1.1681734 CASWeb of Science®Google Scholar V. Trkal, Proc. Camb. Phil. Soc., 21, 80 (1922); CASGoogle Scholar J. H. Van Vleck, Phys. Rev., 22, 547 (1923); 10.1103/PhysRev.22.547 Google Scholar I. C. Percival, J. Phys. A: Math. Nucl. Gen., 7, 794 (1974). 10.1088/0305-4470/7/7/005 Web of Science®Google Scholar I. C. Percival and N. Pomphrey, Molec. Phys., 31, 97 (1976). 10.1080/00268977600100081 CASWeb of Science®Google Scholar I. C. Percival and N. Pomphrey, J. Phys. B (Atom. Molec. Phys.), 9, 3131 (1976). 10.1088/0022-3700/9/17/026 CASWeb of Science®Google Scholar S. Chapman, B. C. Garrett, and W. H. Miller, J. Chem. Phys., 64, (1976). 10.1063/1.432266 CASWeb of Science®Google Scholar A. N. Kolmogorov, Dok. Akad. Nauk, 98, 527 (1954); Google Scholar A. N. Kolmogorov, in Gerretson and de Groot, Eds., Proceedings of the International Congress of Mathematicians Ser. II, 7th Congress, North-Holland, Amsterdam, 1954, Vol. 1, p. 315 (1957) (in Russian). Google Scholar An English translation of this article forms Appendix D of R. Abraham, Foundations of Mechanics, W. A. Benjamin, New York, 967. Google Scholar V. I. Arnol'd, Iz. Akad. Nauk ser Matem, 25, 21 (1961); Google Scholar V. I. Arnol'd, Usp. Matem. Nauk, 18, No. 5, 13 (1963) [English translation, Russian Math. Surv., 18, No. 5, 9 (1963)]; Google Scholar V. I. Arnol'd, Usp. Matem. Nauk, 18, No. 6, 91 (1963) Google Scholar [English translation, Russian Math. Surv., 18, No. 6, 85 (1963)]; 10.1070/RM1963v018n06ABEH001143 Google Scholar J. Moser, Nachr. Akad. Wiss. Göttingen, No. 1, 1 (1962). Google Scholar V. I. Arnol'd and A. Avez, Ergodic Problems of Classical Mechanics, New York, W. A. Benjamin, 1968; Google Scholar C. L. Siegel and J. K. Moser, Lectures on Celestial Mechanics, Springer, Berlin, 1971; 10.1007/978-3-642-87284-6 Google Scholar J. Ford, Lectures in Statistical Physics, Vol. II, W. C. Schieve, Ed., Springer, New York, 1972; Google Scholar L. Galgani and A. Scotti, Revista Nuovo Cimento, 2, 189 (1972); 10.1007/BF02747780 Google Scholar G. H. Walker and J. Ford, Phys. Rev., 188, 416 (1969). 10.1103/PhysRev.188.416 Web of Science®Google Scholar R. A. Marcus, Faraday Disc. Chem. Soc., 55, 34 (1973); 10.1039/dc9735500034 CASWeb of Science®Google Scholar I. C. Percival, J. Phys. B (Atom. Mol. Phys.) 6 L229 (1973); 10.1088/0022-3700/6/9/002 Web of Science®Google Scholar K. S. J. Nordholm and S. A. Rice, J. Chem. Phys., 61, 203 (1974); 10.1063/1.1681624 Web of Science®Google Scholar J. Chem. Phys., 61, 768 (1974). 10.1063/1.1682016 CASWeb of Science®Google Scholar I. E. Fermi, J. Pasta, and S. Ulam, Los Alamos Report LA-1940 (1955), in Enrico Fermi, Collected Works, University of Chicago Press, Chicago, Vol. 2, p. 978. Google Scholar K. R. Symon and A. M. Sessler, Proceedings of the CERN Symposium on High Energy Accelerators and Pion Physics, CERN, Geneva, 1956, Vol. 1, p. 44. Google Scholar E. Thiele and D. J. Wilson, J. Chem. Phys., 35, 1256 (1961); 10.1063/1.1732032 CASWeb of Science®Google Scholar D. L. Bunker, J. Chem. Phys., 37, 393 (1962). 10.1063/1.1701333 CASWeb of Science®Google Scholar M. Hénon and C. Heiles, Astron. J., 69, 73 (1964); 10.1086/109234 Web of Science®Google Scholar G. Contopoulos, Astrophys. J., 138, 1297 (1963); 10.1086/147724 Web of Science®Google Scholar G. Contopoulos, Astron. J., 75, 96 (1970); 10.1086/110948 Web of Science®Google Scholar Astron. J., 76, 147 (1971); 10.1086/111098 Web of Science®Google Scholar J. Ford, Advan. Chem. Phys., 24, 155 (1973). 10.1002/9780470143766.ch3 CASGoogle Scholar J. Ford and G. H. Lunsford, Phys. Rev. A, 1, 59 (1970). 10.1103/PhysRevA.1.59 Web of Science®Google Scholar V. I. Arnol'd, Russian Math. Surv., 18, No. 6, 85 (1963). 10.1070/RM1963v018n06ABEH001143 Google Scholar G. H. Walker and J. Ford, Phys. Rev., 188, 416 (1969). 10.1103/PhysRev.188.416 Web of Science®Google Scholar Ya. G. Sinai, Izv. Akad. Nauk. SSSR Ser. Mat., 30, 15 (1966): Google Scholar Amer. Math. Soc. Transl., 68, 34 (1968). Google Scholar I. C. Percival, Ref. 24; Google Scholar I. C. Percival and N. Pomphrey, Ref. 19. Google Scholar N. Pomphrey, J. Phys. B (Atom. Mol. Phys.), 7, 1909 (1974). 10.1088/0022-3700/7/14/015 CASWeb of Science®Google Scholar B. Barbanis, Astron. J., 71, 415 (1966). 10.1086/109946 Web of Science®Google Scholar A. Norcliffe and I. C. Percival, J. Phys. B (Atom. Mol. Phys.), 1, 774 (1968); 10.1088/0022-3700/1/5/303 Web of Science®Google Scholar C. L. Pekeris, Proc. Symp. Appl. Math. 2, 71 (1950). 10.1090/psapm/002/0034235 Google Scholar M. C. Gutzwiller, J. Math. Phys., 8, 1979 (1967); 10.1063/1.1705112 CASWeb of Science®Google Scholar J. Math. Phys., 10, 1004 (1969); 10.1063/1.1664927 Web of Science®Google Scholar J. Math. Phys., 11, 1791 (1970); 10.1063/1.1665328 Google Scholar J. Math. Phys., 12, 343 (1971); 10.1063/1.1665596 Web of Science®Google Scholar W. H. Miller, J. Chem. Phys., 56, 38 (1972). 10.1063/1.1676877 CASWeb of Science®Google Scholar A. Norcliffe, I. C. Percival, and M. J. Roberts, J. Phys. B (Atom. Mol. Phys.), 2, 578 (1969); 10.1088/0022-3700/2/5/311 Web of Science®Google Scholar A. Norcliffe, Case Studies Atom. Phys., 4, 1 (1973). CASGoogle Scholar R. Balian and C. Bloch, Ann. Phys. (N. Y.), 85a, 514 (1974). 10.1016/0003-4916(74)90421-7 Web of Science®Google Scholar References 2 and 4; Google Scholar P. Pechukas, J. Chem. Phys., 57, 5577 (1972); 10.1063/1.1678259 CASWeb of Science®Google Scholar W. H. Miller, Ref. 41. Google Scholar M. V. Berry and M. Tabor, Proc. Roy. Soc. (London) Ser. A, 349, 101 (1976); 10.1098/rspa.1976.0062 Web of Science®Google Scholar see also W. H. Miller, J. Chem. Phys., 63, 996 (1975). 10.1063/1.431410 CASWeb of Science®Google Scholar Citing Literature Advances in Chemical Physics, Volume 36 ReferencesRelatedInformation

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