De Broglie postulate

Electron diffraction In 1924, de Broglie postulated his principle of wave-particle duality. Just as radiation displays particle-like characteristics, so matter should display wave-Uke characteristics. It followed, therefore, from eqs (22) and (2.7) that a particle with energy, E, and momentum, p, has associated with it an angular frequency, , and wave vector, k, which are given by... 

Lohman, electrode potential, 1457 London forces. 896 Long range interactions, 936 Lorenz and Salie, and partial charge transfer, 922 Lorenz, 1313, 1497 Louis de Broglie postulate. 788 Low energy electron diffraction (LEED), 788, 787, 790... 

Equation 1.19 was derived using equations applicable to the photon, which is massless and has a fixed velocity c. De Broglie postulated that the equation should also apply to particles of matter with mass m and velocity u. Substituting the expression for the momentum of a particle (p = mu) into Equation 1.19 gives the de Broglie relation for the wavelength of a particle ... 

In his doctoral dissertation de Broglie postulated that particles such as the electron, proton, etc. should also possess wave-like properties in exact analogy with the particle-like properties exhibited by electromagnetic waves in the quantum theory of radiation. For motion in one dimension he postulated that the momentum of the particle p and its kinetic energy E were related to the wavevector k and angular frequency w of the guiding wave, I, by the relations... 

Louis de Broglie postulated wave-particle duality in which particles of matter such as protons and electrons would at times display wave-like properties (equation 8.10). Because of an inherent uncertainty of the position and momentum of a wave-like particle, Heisenberg postulated that we cannot simultaneously know a subatomic particle s precise momentum and its position, a proposition referred to as the Heisenberg uncertainty principle (expression 8.11). 

The underlying principle of RHEED is that particles of matter have a wave character. This idea was postulated by de Broglie in (1924). He argued that since photons behave as particles, then particles should exhibit wavelike behavior as well. He predicted that a particle s wavelength is Planck s constant h divided by its momentum. The postulate was confirmed by Davisson and Germer s experiments in 1928, which demonstrated the diffraction of low-energy electrons from Ni. ... 

When Davisson and Germer reported in 1927 that the elastic scattering of low-energy electrons from well ordered surfaces leads to diffraction spots similar to those observed in X-ray diffraction [2.238-2.240], this was the first experimental proof of the wave nature of electrons. A few years before, in 1923, De Broglie had postulated that electrons have a wavelength, given in A, of ... 

Scientists in the 1920s, speculating on this problem, became convinced that an entirely new approach was required to treat electrons in atoms and molecules. In 1924 a young French scientist, Louis de Broglie (1892-1987), in his doctoral thesis at the Sorbonne made a revolutionary suggestion. He reasoned that if light could show the behavior of particles (photons) as well as waves, then perhaps an electron, which Bohr had treated as a particle, could behave like a wave. In a few years, de Broglie s postulate was confirmed experimentally. This led to the development of a whole new discipline, first called wave mechanics, more commonly known today as quantum mechanics. 

The concept that matter possesses both particle and wave properties was first postulated by de Broglie in 1925. He introduced the equation A = hlmv, which indicates a mass (m) moving with a certain velocity (v) would have a specific wavelength (A) associated with it. (Note that this v is the velocity not v the frequency.) If the mass is very large (a locomotive), the associated wavelength is insignificant. However, if the mass is very small (an electron), the wavelength is measurable. The denominator may be replaced with the momentum of the particle (p = mv). 

Similarly, can be used to suggest a way out of the de Broglie paradox [42], which points out that momentum and energy transform differently under Lorentz transformation from frequency. This paradox led de Broglie to postulate the existence of empty waves, which, however, have never been observed empirically. It can therefore be suggested that the Lorentz frequency transform must always be applied to... 

Two main ideas are related to the development of this technique. The first one is the wave nature of the matter. As postulated by Louis de Broglie in 1924, a free electron with mass m, moving with speed v, has a wavelength % related to its momentum (p = mv) in exactly the same way as for a photon, that is,... 

A significant change in the theoretical treatment of atomic structure occurred in 1924 when Louis de Broglie proposed that an electron and other atomic particles simultaneously possess both wave and particle characteristics and that an atomic particle, such as an electron, has a wavelength X = h/p = h/mv. Shortly thereafter, C.J, Davisson and L.H. Germer showed experimentally the validity of this postulate. Dc Broglie s assumption that wave characteristics are inherent in every atomic particle was quickly followed by the development of quantum mechanics, in its most simple form, quantum mechanics introduces the physical laws associated with the wave properties of electromagnetic radiation into the physical description of a system of atomic particles. By means of quantum mechanics a much more satisfactory explanation of atomic structure can be developed. 

In the spirit of Lorentz [45], de Broglie, and Vigier, let us postulate the existence of a preferred frame E. Operationally, E may be identified with the frame of cosmic background radiation (CBR), whose isotropic thermal nature was established by measurements during the COBE-FIRAS project [46]. Then, the principle of relativity simply states that all frames that are not accelerated relative to E, are equivalent to it. 

The observation that the wavelength of light is linked to the particle-like momentum of a photon prompted de Broglie to postulate the likelihood of an inverse situation whereby particulate objects may exhibit wave-like properties. Hence, an electron with linear momentum p could under appropriate conditions exhibit a wavelength A = h/p. The demonstration that an electron beam was diffracted by periodic crystals in exactly the same way as X-radiation confirmed de Broglie s postulate and provided an alternative description of the electronic stationary states on an atom. Instead of an accelerated particle the orbiting electron could be described as a standing wave. To avoid self-destruction by wave interference it is necessary to assume an... 

Wave/particle duality is the postulate that all objects of physical reality possess both localized (particle) and distributed (wave) properties. Due to their low rest mass, electrons exhibit both particle and wave behavior on the scale of length of atoms (nanometers). Thus, every electron has a wavelength associated with it. This wavelength is called the de Broglie wavelength Adb,... 

L. de Broglie (1924) suggested that it might be useful to associate wave-like behavior with the motion of a particle. He postulated that a particle with linear momentum p be associated with a wave whose wavelength A is given by... 

The matter field was originally postulated by Louis de Broglie, and discovered in the electron diffraction studies of Davisson and Germer [30] and of G. P. Thomson [31]. From Schrodinger s understanding of the matter field of, say, an electron, it must be represented in the source terms (charge and current density) of Maxwell s equations, as the moduli of these waves. 

The answers to the above questions, not all of which need he presented here, were formulated between 1925 and 1926, in the revolution of modern quantum theory, which shook the foundations of physics and philosophy. Remarkably, the central theme of quantum theory was the nature of light, and what came to be called the wave-particle duality. But other broader implications of the new theory existed, and the first inkling of this was given in 1924 by Louis de Broglie (Fig. 3.26) in his doctoral dissertation. He postulated that particles may also possess wavelike properties and that these wavelike properties would manifest themselves only in phenomena occurring on an atomic scale, as dictated by Planck s constant. He also postulated that the wavelength of these matter waves, for a given particle such as an electron or proton, would be inversely proportional to the particle s momentum p, which is a product of its mass m and speed... 

In 1903, Marie Curie, her husband and Henri Becquerel received the Nobel Prize in physics Marie won another Nobel prize (chemistry) in 1911. In 1900, Max Planck had postulated that light energy must be emitted and absorbed in discrete particles, called quanta. In Paris in 1924, Victor de Broglie concluded that if light could act as if it were a stream of particles, particles could have the properties of waves. Both quanta and waves are central to quantum physics. Quantum theory states that energy comes in discrete packets, called quanta, which travel in waves. The principle of wave-particle duality states that all subatomic particles can be considered as either waves or particles. Light is a stream of photon particles that travel in waves. 

The solution, proposed by Einstein, was that the discrete energy units, identified by Planck, correspond to quanta of light, called photons, which interact with electrons in the metal surface during direct collision. This dual wave/particle nature of light inspired de Broglie to postulate a similar behaviour for electrons. Experimental observation of electron diffraction confirmed the wave nature of electrons and firmly estabUshed the dual character of all quantum objects as mysterious reality. As the logical pictme of an entity, which is wave as well as particle, is hard to swallow, it has become fashionable to avoid all physical models of quantum events it is considered poor taste to contaminate the quantmn world with classical concepts. This noble idea of the so-called Copenhagen interpretation of quantmn theory has resulted in a probabilistic computational model that, not only defies, but denies comprehension. 

The postulate of Nagaoka and de Broglie, and the discovery of electron diffraction suggested that the appearance of integer quantum numbers relates to the periodicity of wave motion, which is also characterized by integers, and that the behaviour of quantum particles should be described by the general wave equation, which in one dimension reads ... 

The same result can be obtained equivalently by postulating that an integer number ( ) of the de Broglie... 

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