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Quantum mechanical streamlines. III. Idealized reactive atom–diatomic molecule collision
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8.G. Kriegsman and J. B. Keller (Courant Institute, New York University) are currently preparing a manuscript in which they consider the reflections and transmissions of electromagnetic waves in a two‐dimensional waveguide with a right angle bend. Their problem is therefore analogous to our atom‐diatomic molecule collision problem. In their formulation they use the modern version of the (complex) ray theory of optics [see A. J. W. Sommerfeld, Optics (Academic, New York, 1954);
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8.and H. Y. Yee, L. B. Felsen, and J. B. Keller, SIAM J. Appl. Math. 16, 268 (1968)] which is asemiclassical type of approximation making use of diffraction from the right angle wedges (corresponding to our and corners). Their method of solution becomes accurate at large energies.
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17.L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960) has an excellent discussion of the propagation of signals and a chapter by Sommerfeld which includes his treatment of the “forerunners.” This treatment is pertinent with respect to any attempt to interpret time delays when the de Broglie wavelength is long compared to the length of the interactive zone.
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