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2002 | 101 | 3 | 369-385
Article title

On the Extinction Paradox

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EN
Abstracts
EN
The extinction paradox, the difference of classical and quantum scattering cross-sections for the scattering of particles by a rigid sphere (σ^Q=2π a^2=2σ^C for ka ≫ 1), is analyzed in a simpler 2D model of a rigid cylindrical potential. Rigorous solutions of the Schrödinger equation for particle beams, including also finite width beams, are derived and employed in the description of the scattering process. The scattering particle fluxes, with a thorough treatment of the forward directions, are being studied. It is pointed out that for wide beams (w ≫ a) the scattered flux can reach the value determined by the quantum theory, provided that it is measured at distances R ≫ waλ. Moderately narrow beams (1≪ w≪ a) behave as classical trajectories, and their scattering can be described in classical terms. Thus, the classical limit of quantum scattering requires not only that the de Broglie wavelength λ_B is much smaller than the size of the scatterer (a ≫ λ_B), but also that the transverse width of beams of de Broglie's waves is small, w≪ a.
Keywords
EN
Publisher

Year
Volume
101
Issue
3
Pages
369-385
Physical description
Dates
published
2002-03
received
2001-06-20
Contributors
author
  • Institute of Physics, Polish Academy of Sciences, al. Lotników 32/46, Warsaw 02-668, Poland
References
  • 1. A. Messiah, Quantum Mechanics, Interscience, New York 1961
  • 2. L.I. Schiff, Quantum Mechanics, McGraw-Hill, New York 1968
  • 3. I. Bialynicki-Birula, M. Cieplak, J. Kaminski, Theory of Quanta, Oxford University Press, Oxford 1992
  • 4. N.F. Mott, H.S.W. Massey, The Theory of Atomic Collisions, Clarendon Press, Oxford 1965
  • 5. R.G. Newton, Scattering Theory of Waves and Particles, 2nd ed., Springer-Verlag, New York 1982
  • 6. H.S.W. Massey, C.B.O. Mohr, Proc. R. Soc. A, 141, 434, 1933
  • 7. J.D. Jackson, Classical Electrodynamics, Wiley, New York 1962
  • 8. J.O. Hirschfelder, K.T. Tang, J. Chem. Phys., 65, 470, 1976
  • 9. W. Zakowicz, submitted to Phys. Rev. E
  • 10. D.H. Perkins, Introduction to High Energy Physics, Polish Scientific Publishers PWN, Warsaw 1989 (in Polish)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv101n306kz
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