Abstract
The time-dependent scattering of one-dimensional Gaussian wave packets of various energies incident on(1) a square potential barrier and(2) a square well is examined numerically, using the quantum potential introduced by Bohm. The time-dependent quantum potential is calculated in each case, and the results displayed on three-dimensional computer plots. The particle trajectories from different initial positions within the wave packet are also shown, giving a detailed description of reflection and tunneling in terms of individual processes. The wider implications of this analysis are also briefly considered.
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References
C. Philippidis, C. Dewdney, and B. J. Hiley,Nuovo Cimento 52B, 15 (1979).
R. D. Prosser,Int. J. Theoret. Phys. 15, 169, 181 (1976).
A. Goldberg, H. M. Schey, and J. L. Schwarts,Am. J. Phys. 35, 177 (1967).
D. J. Bohm,Phys. Rev. 85, 180 (1952).
L. de Broglie,Une Interprétation Causale et Non Linéaire de la Mécanique Ondulatoire la Théorie de la Double Solution (Gauthier-Villars, Paris, 1956) [English translation, Elsevier, Amsterdam, 1960].
F. J. Belinfante,Measurements and Time Reversal in Objective Quantum Theory (Pergamon, Oxford, 1975).
D. J. Bohm, private communication.
A. Einstein,The Born-Einstein Letters (MacMillan, London, 1971).
W. Pauli, inLouis de Broglie: Physicien et Penseur, A. George, ed. (Michel, Paris, 1953).
D. J. Bohm and B. J. Hiley,Found. Phys. 5, 93 (1975).
A. Baracca, D. J. Bohm, B. J. Hiley, and A. E. G. Stuart,Nuovo Cimento 28B, 453 (1975).
J. P. Vigier,Lett. Nuovo Cimento 29, 467 (1980).
J. O. Hirschfelder and A. C. Christoph,J. Chem. Phys. 61, 5435 (1974).
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Dewdney, C., Hiley, B.J. A quantum potential description of one-dimensional time-dependent scattering from square barriers and square wells. Found Phys 12, 27–48 (1982). https://doi.org/10.1007/BF00726873
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DOI: https://doi.org/10.1007/BF00726873