Abstract
For an arbitrary potential V with classical trajectoriesx=g(t), we construct localized oscillating three-dimensional wave lumps ψ(x, t,g) representing a single quantum particle. The crest of the envelope of the ripple follows the classical orbitg(t), slightly modified due to the potential V, and ψ(x, t,g) satisfies the Schrödinger equation. The field energy, momentum, and angular momentum calculated as integrals over all space are equal to the particle energy, momentum, and angular momentum. The relation to coherent states and to Schrödinger waves is also discussed.
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References
M. Born,Z. Phys. 37, 863 (1926;38, 803 (1926.)
A. O. Barut,Phys. Lett. A 143, 349 (1990).
A. O. Barut and A. Grant,Found. Phys. Lett. 3, 303 (1990).
For a historical discussion, see A. O. Barut, “Louis de Broglie and the single quantum particle,” in L. de Broglie,Heisenberg's Uncertainties and the Probabilistic Interpretation of Wave Mechanics, translation by A. van der Merwe (Kluwer, Dordrecht, 1990).
E. Schrödinger,Naturwissenschaften 14, 664 (1926).
The distinction between ψ(x,t;g) and ψ(x,t) is discussed in A. O. Barut,Found. Phys. Lett. 1, 47 (1988) and Ref. 4, and the passage from one to the other in A. O. Barut, in “Symposium on the Foundations of Modern Physics 1990” (Joensuu, Finland), World Scientific.
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Barut, A.O. Quantum theory of single events: Localized De Broglie wavelets, Schrödinger waves, and classical trajectories. Found Phys 20, 1233–1240 (1990). https://doi.org/10.1007/BF01889467
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DOI: https://doi.org/10.1007/BF01889467