De Broglie matter wave

The group velocity of de Broglie matter waves are seen to be identical with particle velocity. In this instance it is the wave model that seems not to need the particle concept. However, this result has been considered of academic interest only because of the dispersion of wave packets. Still, it cannot be accidental that wave packets have so many properties in common with quantum-mechanical particles and maybe the concept was abandoned prematurely. What it lacks is a mechanism to account for the appearance of mass, charge and spin, but this may not be an insurmountable problem. It is tempting to associate the rapidly oscillating component with the Compton wavelength and relativistic motion within the electronic wave packet. 

In this chapter we explored the question of how to use the De Broglie matter waves to describe... 

In order to describe microscopic systems, then, a different mechanics was required. One promising candidate was wave mechanics, since standing waves are also a quantized phenomenon. Interestingly, as first proposed by de Broglie, matter can indeed be shown to have wavelike properties. However, it also has particle-Uke properties, and to properly account for this dichotomy a new mechanics, quanmm mechanics, was developed. This chapter provides an overview of the fundamental features of quantum mechanics, and describes in a formal way the fundamental equations that are used in the construction of computational models. In some sense, this chapter is historical. However, in order to appreciate the differences between modem computational models, and the range over which they may be expected to be applicable, it is important to understand the foundation on which all of them are built. Following this exposition. Chapter 5 overviews the approximations inherent... 

Louis de Broglie proposes wave nature of matter. 

In the mind of de Broglie, the wave accompanies the particle. He also talked about a pilot wave that guided the particle in its path. It is unclear in the theory of de Broglie what the physical meaning of the matter wave is. Is it a longitudinal wave like sound waves How then could waves appear in a vacuum The meaning of the waves was not cleared up until the interpretation of Max Born some years later. 

The problem with interpretation of this idea of matter waves is that waves should exhibit diffraction which is not commonly observed macroscopically. Consider a typical rifle buUet of 4.2 g traveling at a speed of 965 m/sec. The De Broglie matter wavelength for that buUet would be... 

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 miderstanding of molecular motions is necessarily based on quaiitum mechanics, the theory of microscopic physical behaviour worked out in the first quarter of the 20th century. This is because molecules are microscopic systems in which it is impossible—or at least very dangerous —to ignore the dual wave-particle nature of matter first recognized in quaiitum theory by Einstein (in the case of classical waves) and de Broglie (in the case of classical particles). 

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. ... 

The first consistent attempt to unify quantum theory and relativity came after Schrddinger s and Heisenberg s work in 1925 and 1926 produced the rules for the quantum mechanical description of nonrelativistic systems of point particles. Mention should be made of the fact that in these developments de Broglie s hypothesis attributing wave-corpuscular properties to all matter played an important role. Central to this hypothesis are the relations between particle and wave properties E — hv and p = Ilk, which de Broglie advanced on the basis of relativistic dynamics. 

Erwin Schrodinger (1887-1961 Nobel Prize for physics 1932) transferred the concept of wave-particle duality of matter developed by L. V. de Broglie for electrons to the whole atom and thus developed wave mechanics. The Schrodinger equation allows a description of orbitals as the probability of the location of the electrons. Wave mechanics represented a significant development, but were subsequently shown to be insufficient. 

In 1923 de Broglie made the bold suggestion that matter, like light, has a dual nature in that it sometimes behaves like particles and sometimes like waves. He suggested that material (i.e., non-zero-rest mass) particles with a momentum p = mv should have wave properties and a corresponding wavelength given by... 

Schrodinger s equation is widely known as a wave equation and the quantum formalism developed on the basis thereof is called wave mechanics. This terminology reflects historical developments in the theory of matter following various conjectures and experimental demonstration that matter and radiation alike, both exhibit wave-like and particle-like behaviour under appropriate conditions. The synthesis of quantum theory and a wave model was first achieved by De Broglie. By analogy with the dual character of light as revealed by the photoelectric effect and the incoherent Compton scattering... 

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). 

By the early 1920s, it was standard knowledge that energy had matter-like properties. In 1924, a young physics student named Louis de Broglie stated a hypothesis that followed from this idea. What if, de Broglie wondered, matter has wave-like properties ... 

De Broglie s hypothesis of matter waves received experimental support in 1927. Researchers observed that streams of moving electrons produced diffraction patterns similar to those that are produced hy waves of electromagnetic radiation. Since diffraction involves the transmission of waves through a material, the observation seemed to support the idea that electrons had wave-like properties. 

A class of partial differential equations first proposed by Erwin Schrodinger in 1926 to account for the so-called quantized wave behavior of molecules, atoms, nuclei, and electrons. Solutions to the Schrodinger equation are wave functions based on Louis de Broglie s proposal in 1924 that all matter has a dual nature, having properties of both particles and waves. These solutions are... 

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... 

The starting point of de Broglie s theory is the belief that the reality is observer-independent even if the observer interacts and therefore modifies in greater or lesser degree the external reality. Therefore in this model it is assumed that the matter waves are real physical waves different from the common statistical wave , Active and arbitrarily normalized. This real wave is composed of an extended, yet finite wave 0, plus a singularity , such that... 

Another possibility [16,17] for testing the reality of the quantum waves derives directly from de Broglie causal theory. As we have seen, in this approach, the quantum particle is composed of a wave plus a singularity. These two composing entities have different properties when interacting with matter or with the surrounding subquantum medium. 

A second interpretation of the Aharonov-Bohm effect was devised by Boyer [65,66], who used matter waves associated to moving electrons. Waves coming from each slit interfere with a phase shift = 2jidistance between two slits. If P is the impulse of an electron in the beam, the de Broglie relation gives us P 2nh/X. This results in the fact that the phase... 

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