Abstract
Computer portrayals are presented of a one-dimensional model of fundamental particles as developed by U. Enz from the breather solution of the nonlinear sine-Gordon equation in the context of soliton physics. Particles portrayed are the stationary and the moving basic nucleon and the stationary electron. The portrayals illustrate the nonlinear characteristics of the u wave anticipated by de Broglie as part of his proposed “double solution” in wave mechanics. Linear plots of u vs x for a moving breather exhibit the familiar single hump profile which moves with group velocity v g = ßc. Plots of the signed logarithm of u vs x reveal both an apex corresponding to the single hump of the linear plot plus the de Broglie | waves which are strongly modulated by the exponential decrease (~ 43 decades per de Broglie wavelength) and which move with phase velocity v p = c/ß. The semilogarithmic plot makes possible a unique portrayal of the wave packet representing a moving particle which shows the coexistence of both particle and wave.
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References
L. L. de Broglie, Non-Linear Wave Mechanics (Elsevier, New York, 1960).
U. Enz, Physica 17D, 116 (1985).
U. Enz, Physica 21D, 1 (1986).
N. J. Zabusky and M . D. Kruskal, Phys. Rev. Lett 15, 240 (1965).
G. L. Lamb, Jr., Elements of Soliton Theory (Wiley, New York, 1980).
G. Eilenberger, Solitons: Mathematical Methods for Physicists (Springer, Berlin, 1981).
The profiles in Ref. 5 are credited to Ch. Poppe, Diplomarbeit ,Universität Heidelberg, 1977. They are actually derivatives of the breather potential.
P. G. Drazin and R. S. Johnson, Solitons: An Introduction (Cambridge University Press, Cambridge, 1989).
J. Rubinstein, J. Math. Phys. 11, 258 (1970).
M. J. Ablowitz et al, Phys. Rev. Lett. 30, 1262 (1973).
G. Lochak, in The Wave-Particle Dualism ,S. Diner et al., eds. (Reidel, Dordrecht, 1983).
L. de Broglie, Compt. Rend. Acad. Sci. 177, 507, 548, 630 (1923).
A. O. Barut and P. Rusu, Can. J. Phys. 67, 100 (1989).
A. 0. Barut, Found. Phys. 20, 1233 (1990).
A. O. Barut and A. J. Bracken, Found. Phys. 22, 1267 (1992).
L. de Broglie, Probl èmes de Propagations Guidées des Ondes Électromagnétiques (Gauthiers-Villars, Paris, 1941).
A. J. Hatch, Standing-Wave Model of Nuclear Structure (1983, unpublished).
A. J. Hatch, Binding Energy of Superposed Standing Waves (1983, unpublished).
A. J. Hatch, Calculation of Nuclear Radii (1984, unpublished).
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© 1994 Springer Science+Business Media New York
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Hatch, A.J. (1994). Computer Portrayals of the Sine-Gordon Breather as a Model of the de Broglie Double Solution. In: van der Merwe, A., Garuccio, A. (eds) Waves and Particles in Light and Matter. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2550-9_44
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DOI: https://doi.org/10.1007/978-1-4615-2550-9_44
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