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Mathematical Preparation and Rules of Tracing

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Semiclassical Theories of Molecular Scattering

Part of the book series: Springer Series in Chemical Physics ((CHEMICAL,volume 26))

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Abstract

Few equations of motion are solvable in terms of known analytic functions in physics and chemistry. We are often compelled to look for some approximate solutions or physical models which yield exactly solvable equations since they furnish more insight into the nature of the system of interest than the exact, but numerical solutions. Frequently, approximations are made on physical rather than on mathematical grounds. Of course, this does not mean that mathematics is completely ignored.

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References

  1. H. Poincaré: Acta Math. VIII, 295 (1886)

    Article  Google Scholar 

  2. E.T. Whittaker, G.N. Watson: Modern Analysis, 4th ed. (Cambridge University Press, London 1952)

    Google Scholar 

  3. G.G. Stokes: Trans. Cambridge Philos. Soc. 9, 165 (1856);

    Google Scholar 

  4. G.G. Stokes: Trans. Cambridge Philos. Soc. 10, 105 (1857);

    ADS  Google Scholar 

  5. G.G. Stokes: Trans. Cambridge Philos. Soc. 11, 412 (1871)

    Google Scholar 

  6. P.M. Morse, H. Feshbach: Methods of Theoretical Physics (McGraw-Hill, New York 1953)

    MATH  Google Scholar 

  7. H. Jeffreys: Asymptotic Approximations (Oxford University Press, London 1962)

    MATH  Google Scholar 

  8. A. Erdelyi: Asymptotic Expansions (Dover, New York 1956)

    MATH  Google Scholar 

  9. J. Liouville: J. Math. Pures Appl. 2, 16 (1837)

    Google Scholar 

  10. J. Horn: Math. Ann. 52, 271 (1899)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lord Rayleigh: Proc. R. Soc. London, Ser. A86, 207 (1912)

    Article  ADS  Google Scholar 

  12. G. Wentzel: Z. Phys. 38, 518 (1926)

    Article  ADS  Google Scholar 

  13. H.A. Kramers: Z. Phys. 39, 828 (1926)

    Article  ADS  Google Scholar 

  14. M.L. Brillouin: J. Phys. Radium 7, 353 (1926)

    Article  Google Scholar 

  15. G.N. Watson: Theory of Bessel Functions (Cambridge University Press, London 1966)

    MATH  Google Scholar 

  16. M. Abramowitz, I.A. Stegun: Handbook of Mathematical Functions (NBS, Washington, DC 1964)

    MATH  Google Scholar 

  17. J. Heading: An Introduction to Phase Integral Methods (Methuen, London 1962)

    MATH  Google Scholar 

  18. A. Zwaan: Intensitäten im Ca-Funkenspectrum, Ph.D. Dissertation, Utrecht (1929)

    Google Scholar 

  19. E.C. Kemble: The Fundamental Principles of Quantum Mechanics (McGraw-Hill, New York 1937)

    Google Scholar 

  20. R.E. Langer: Bull. Amer. Math. Soc. (2) 40, 545 (1934);

    Article  MathSciNet  Google Scholar 

  21. R.E. Langer: Phys. Rev. 51, 669 (1937);

    Article  ADS  MATH  Google Scholar 

  22. R.E. Langer: Commun. Pure Appl. Math. 3, 427 (1950);

    Article  MATH  Google Scholar 

  23. R.E. Langer: Trans. Am. Math. Soc. 84, 144 (1957)

    Article  MATH  Google Scholar 

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© 1984 Springer-Verlag Berlin Heidelberg

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Eu, B.C. (1984). Mathematical Preparation and Rules of Tracing. In: Semiclassical Theories of Molecular Scattering. Springer Series in Chemical Physics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88165-7_2

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  • DOI: https://doi.org/10.1007/978-3-642-88165-7_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-88167-1

  • Online ISBN: 978-3-642-88165-7

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