Wave-particle dualism

Following Atkins [68], the propagation of particles follows a path dictated by Newton s laws, equivalent to Hamilton s principle, that particles select paths between two points such that the action associated with the path is a minimum. Therefore, Fermat s principle for light propagation is Hamilton s principle for particles. The formal definition of action is an integral identical in structure with the phase length in physical optics. Therefore, particles are associated with wave motion, the wave-particle dualism. Hamilton s principle of least... 

P. W. Milloni, The Wave Particle Dualism—a tribute to Louis De Broglie on his 9Cfh Birthday, Reidel, Dordrecht, 1984. 

C. Dewdney, P. Gueret, A. Kyprianidis, and J. P. Vigier, Testing wave particle dualism with time dependent neutron interferometry, Phys. Lett. A 102A(7), 291-294 (1984). 

IHow perfect needs to be the lattice In fact, the high order of a perfect crystalline lattice facilitates the mathematical modeling of a solid material. Thus, a crystal can be described by the oscillations of the lattice, that is, by the phonon spectrum (wave-particle dualism). 

Schrodinger and Bohm both accepted that quantum motion follows a wave pattern. To account for wave-particle dualism the interpretation of matrix mechanics, developed by Heisenberg and others, was extended on the assumption of probability densities. Schrodinger developed the notion of wave structures to simulate particle behaviour, but this model has been rejected almost universally and apparently irretrievably, in favour of proba-bities, arguably prematurely and for questionable reasons. Bohm s attempt to revive the wave interpretation advocated a literary interpretation of wave-particle dualism in the form of a classical particle accompanied and piloted by a quantum wave. 

With some linguistic precautions connected with the wave-particle dualism of quantum mechanics, the electron density g can be interpreted... 

There is a principal difference that complicates the direct use of the operation approach to the problem of localizing photons in the case of multipole radiation. The point is that the multipole photons are in a state with given angular momentum and therefore they have no well-defined direction of propagation. In view of the wave-particle dualism, one can say that the multipole photons emitted by a point-like quantum source propagate as outgoing spherical waves. Definitely, these photons are localized initially inside the source. 

Mental models pattern of atoms, ions, molecules o electrons, wave-particle, dualism... 

From the view of classical mechanics a microscopic particle, e.g. an electron, cannot traverse a potential barrier which is higher than its kinetic energy. Using quantum mechanics, however, we know that this is possible due to the wave-particle dualism. The probability to find the electron on the other side of the barrier is not equal to zero if it impinges the barrier. The transmission coefficient T representing the ratio of transmitted and incident current is given by... 

F. Falciglia, L. Fornari, A. Garuccio, G. laci, and L. Pappalardo, in The Wave-Particle Dualism (edited by S. Diner, G. Lochak, and F. Selleri), pp. 397-412, D. Reidel, Dordrecht... 

Several possibilities of formulating these postulates exist. The collection and presentation of postulates which we consider useful for the development of a relativistic many-electron theory are given in the following sections. Also, we avoid any discussion of the wave-particle dualism of matter since we are interested in the presentation of a formalism that eventually allows us to describe and predict matter on a molecular scale. It is thus most convenient to think of electrons and atomic nuclei simply as particles rather than as waves. The following sections introduce five basic axioms of quantum theory. 

In exactly the same way, an absolutely asymmetrical world is impossible to find too. Behind almost every discovery and its attempts, the driving force was the sense of symmetry and the efforts to establish that. We can site numerous examples like Maxwell s displacement current to wave particle dualism and also to De Broglie s finding of electron wave. 

Wheaton, B. R. (1983). The tiger and the shark Empirical roots of wave-particle dualism. Cambridge Cambridge University Press. 

A succinct description of the quantum physics fundamentals is presented in Chapter 2. I recall particle-wave dualism, uncertainty principle, concepts of wave motion. The wave function and the Schrodinger equation and an abstract notion of k-space are discussed. 

In 1924 Louis de Broglie, struck by the dualism of the particle and wave nature of light, argued that if a photon of radiation had momentum given by p = hv/c = hj, then maybe a mass particle had a wave nature where A = h/p = h/mv. So one can see that Bohr s... 

If. The Dual Nature of Light. /The essential feature of quantum mechanics is the dualism of all the fundamental particles. At times these particles behave like forms of wave motion at other times they exhibit the ordinary properties of particles. Consider, for example, the photon. Although Einstein was forced to assume that the energy of a light wave was concentrated into corpuscles, his success in explaining the photoelectric effect in no way invalidated the old well-tested evidence that light is a form of wave motion. It is just as inconceivable that a stream of particles should show the phenomena of diffraction as that a wave should suddenly concentrate its energy at one point to knock an electron out of a surface. 

Thus in the phenomena described, radiation is represented by a flow of corpuscles, quanta of energy which have been called photons. The energy of each photon is defined by product hco. Though for a long time it was known that in other experiments the same radiation manifests itself as a flow of waves. There is a problem, which has occupied the minds of many physicists, which is now known as particle-wave dualism and to which we shall pay more attention. 

Thereby, the de Broglie hypothesis has been widely accepted as a scientific law. To reiterate, particle-wave dualism is one of the cornerstones of quantum mechanics. 

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