It was shown that for explanation of experimental results on diffraction of micro particles it does no need to use the de Broglie wave’s concept. Such the results can be described with the aid of the Heisenberg uncertainties relation. As for examples the known results of experiments conducted by C. Davisson and L. H. Germer on diffraction of electrons and by Rutherford on particles scattering are considered.
It was shown that for explanation of experimental results on diffraction of micro particles it does no need to use the de Broglie wave’s concept. Such the results can be described with the aid of the Heisenberg uncertainties relation. As for examples the known results of experiments conducted by C. Davisson and L. H. Germer on diffraction of electrons and by Rutherford on particles scattering are considered.
This chapter describes the dual nature of electron/de Broglie waves. de Broglie suggested that like light, an electron also behaves as both a particle and a wave. Based on this hypothesis, a relationship between wavelength of electrons (a particle) and momentum was developed. It opines that ‘wavelength of the particle is inversely proportional to momentum’. This is called the de Broglie relation. On the basis of the above facts, we have developed a relationship between wavelength and voltage applied and this relation may be stated as ‘the wavelength of a particle is inversely proportional to the square root of the voltage applied to the system’. This chapter also uses the Davisson and Germer experiment to show the wave nature of the particle, i.e., diffraction of electrons by crystal lattice. The experimental results were the same as found in the case of the diffraction of X-ray by crystals. This chapter also provides an idea on quantisation of angular momentum. It also discusses Heisenberg’s uncertainty principle, phase velocity, group velocity, and uncertainty relation between energy and time. The chapter comprises the experimental evidence of Heisenberg’s uncertainty principle, such as by diffraction of electrons through a slit and gamma ray microscope thought experiment, which is shows the physical significance of the uncertainty principle. Sufficient references, solved problems, and questions on concepts have been provided at the end of chapter.
Abstract In 1925, de Broglie hypothesized that any material particle has an associated wave with /h p . Electron diffraction seems to support that Hypothesis. But then, the electron at rest will have infinite wavelength, and infinite wave phase velocity. This says that for a material particle, the de Broglie relation does not hold. Failed attempts to save the postulate, kept the flawed relation, and modified the waves into train waves, pilot waves, probability waves, … to name a few. We keep the de Broglie waves unchanged, and modify the relation. First, we observe that the Planck energy E h used by de Broglie defines virtual electromagnetic waves. Consequently, for any particle, the virtual electromagnetic wavelength is / /c h mc , and / /h m c . Refinement of de Broglie argument, indicates that /h mmay be x , Heisenberg’s uncertainty in the particle location. de Broglie’s later analysis supports this interpretation, and we offer an explanation to particle diffraction as a consequence of Heisenberg’s uncertainty. We apply / /h m c to obtain the dispersion relations for the de Broglie virtual waves.
espanolEste articulo muestra que el enfoque estocastico para resolver el problema de la dispersion de particulas elementales en el cristal puede servir como una alternativa a la hipotesis de Louis de Broglie sobre las propiedades ondulatorias de las particulas materiales. Los resultados de los calculos presentados en este trabajo concuerdan bien con los patrones de difraccion de electrones y los patrones de difraccion de rayos X obtenidos experimentalmente y los experimentos de Davisson-Germer. EnglishThis paper shows that the stochastic approach to solving the problem of the scattering of elementary particles on crystal can serve as an alternative to Louis de Broglie’s hypothesis on the wave properties of material particles. The results of calculations presented in this work are in good agreement with the experimentally obtained electron diffraction patterns and X-ray diffraction patterns and the Davisson-Germer experiments.
We discuss the breakdown of classical theory in relation to phenomena on the nanoscale. The historical discovery of the wave nature of electrons in the Davisson–Germer Experiment is reviewed. We present the puzzling experimental data and its explanation in terms of particle diffraction, which contradicts classical mechanics. The quantitative success of de Broglie’s formula in associating particle momenta with a wavelength is demonstrated. Analyzing the conditions in which the wave nature of particles becomes apparent, namely, the condition for correspondence between the de Broglie wavelength and the lattice from which the particles are diffracted, we draw some general conclusions. Particularly, by translating to de Broglie wavelengths the particle masses and energy values that are typical to materials and processes on the nanoscales, one immediately realizes that wave properties are expected to be dominant. Quantum mechanics is therefore essential for a proper description of nanoscale phenomena.
In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach to solving the problem of scattering of elementary particles on crystals can serve as an alternative to the Louis de Broglie hypothesis about the wave properties of material particles. The results of calculations by formula (2.2), presented in this pa-per, are in good agreement with the experimentally obtained electron diffraction patterns and X-ray diffraction patterns and the Davisson-Germer experiments.
The chapter presents the first application of wave ideas to quantum particle descriptions, including describing the Davisson–Germer experiment, in which electrons were diffracted as waves from crystals. The work of famous early developers of quantum mechanics—Planck, Einstein, and de Broglie—led to relating momentum to wavelength, and energy to frequency. The wave function and its probability interpretation by Born are introduced. The wave functions of a particle in a box potential are exactly analogous to classical standing waves, giving these matter waves quantized energies just as frequencies are quantized in the harmonic series of a stringed instrument. The Heisenberg uncertainty principle follows from the general wave analysis. Zero-point motion and zero-point energy are important concepts resulting from the application of wave ideas to particles.