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Nonlinear Chemistry

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The Chemistry of Matter Waves

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Abstract

The sensational aspects of quantum theory, from the wave-particle nature of electrons to Schrödinger’s cat, are the artefacts that result from describing nonlinear systems by linear differential equations. As linear waves are dispersive, a wave model of the electron is still being rejected, whereas a nonlinear wave model is shown to account for electronic behaviour in all conceivable situations. This chapter introduces the distinction between linear and nonlinear systems with examples from hydrodynamics and mechanics and applied to the wave mechanics of wave packets, solitons, electrons and lattice phonons. Special topics for discussion include the motion of free electrons, the fine-structure parameter, electron diffraction, photoelectric and Compton effects, X-ray diffraction, metallic conduction, superconductivity and elementary covalent interaction. A new innovation, introduced here, is recognition of the quantum potential as a nonlinearity parameter that enables a seamless transition between classical and non-classical systems.

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Notes

  1. 1.

    Zitterbewegung.

  2. 2.

    At an even earlier date Schrödinger was the first to recognize the phase invariance of electronic motion [40] that subsequently developed into modern gauge theory, the basis of elementary-particle physics, but rarely attributed to the seminal source.

  3. 3.

    It is customary to use the notation u t ≡∂u/∂t, u xx ≡∂ 2 u/∂x 2, etc. in writing nonlinear wave equations.

  4. 4.

    This procedure is analyzed in detail by Toda [43].

  5. 5.

    As pointed out by Goldstein [3, p. 283], the most general transformation in Minkowski space that preserves the velocity of light has the form x′=Lx+a, where a is an arbitrary translation vector of the origin and L is the orthogonal matrix of the homogeneous Lorentz transformation x′=Lx (4.4). The modified inhomogeneous (Poincaré) transformation has ten independent elements compared to the six of (4.4). This condition generates the intrinsic nonlinearity of curved space-time.

  6. 6.

    For details see [31, p. 134].

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  1. Centre for Advancement of Scholarship, University of Pretoria, Pretoria, South Africa

    Jan C. A. Boeyens

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Boeyens, J.C.A. (2013). Nonlinear Chemistry. In: The Chemistry of Matter Waves. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7578-7_7

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