Matter wave character

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. ... 

Matter is classically particulate in nature, but it also manifests wave character. The wave property of matter is related to its particle nature by de Broglie s relation A = hip, where A is known as the de Broglie wave length. 

The development of wave mechanics has been made possible through the introduction by de Broglie of a new principle dealing with the wave character of matter. The basis of this principle is the recognition that different interpretations are appropriate to different kinds of measurements thus atoms and electrons which have hitherto been regarded as discrete particles arc considered to possess a dual character, in the sense that they may possess both corpuscular and wave properties. A duality of a similar kind had been revealed earlier in studies on the propagation of light. 

If matter has wave properties, why are they not commonly observed Calculation using the de Broglie relation shows that a baseball (0.145 kg) moving at about 60 mi/hr (27 m/s) has a wavelength of about 10 m, a value so incredibly small that such waves cannot be detected. On the other hand, electrons moving at only moderate speeds have wavelengths of a few hundred picometers (1 pm = 10 m). Under the proper circumstances, the wave charact of electrons should be observable. 

To this point, we have been content to accept the electron as a particle, a bit of matter. However, Louis de Broglie in 1924 reasoned that since particle properties, as well as wave properties, are associated with light, it is likely that a wave character is associated with a particle, such as an electron, a proton, an atom, a molecule, or a piece of chalk. The wave associated with a particle is called a matter wave. He predicted that the wavelength of a matter wave is... 

Matter exhibits a dual particle-wave character. 

The magnificent implication of these experimental observations is that all matter exhibits both a particulate and a wave character, and de Broglie was the first to quantify the connection of the two characters of matter. 

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... 

But these mathematical tools have to be used in the service of fundamental physical ideas. This opinion had already been expressed by Dirac to maintain physics on the foreground and examinate, as often as possible, the physical sense hidden under the mathematical formalism. [22] In the 1950s, the wave equation was insoluble, except for the molecules of hydrogenic character. As a matter of fact, the chemist introduces just those functions which correspond to the behavior to be expected chemically. [23] Mathematical operations have to be guided In practically the whole of theoretical chemistry, the form in which the mathematics is cast is suggested, almost inevitably, by experimental results. [24]... 

As already pointed out, terms such as wave function, electron orbit, resonance, etc., with which we describe the formulations and results of wave mechanics, are borrowed from classical mechanics of matter in which concepts occur which, in certain respects at least, show a correspondence to the wave mechanical concepts in question. The same is the case with the electron spin. In Bohr s quantum theory, Uhlenbeck and Goudsmit s hypothesis meant the introduction of a fourth quantum number j, which can only take on the values +1/2 and —1/2- In wave mechanics it means that the total wave function, besides the orbital function, contains another factor, the spin function. This spin function can be represented by a or (3, whereby, for example, a describes the state j = +1/2 and P that with s = —1/2. The correspondence with the mechanical analogy, the top, from which the name spin has been borrowed, is appropriate in so far that the laevo and dextro rotatory character, or the pointing of the top in the + or — direction, can be connected with it. A magnetic moment and a... 

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