Wave behavior of matter

THE WAVE BEHAVIOR OF MATTER We recognize that matter also has wave-like properties. As a result, it is impossible to determine simultaneously the exact position and the exact momentum of an electron in an atom (Heisenberg s uncertainty principle). 

WAVE BEHAVIOR OF MATTER (SECTION 6.4) De Broglie proposed that matter, such as electrons, should exhibit wave-like properties. This hypothesis of matter waves was proved experimentally by observing the diffraction of electrons. An object has a characteristic wavelength that depends on its momentum, mv A = h/mv. 

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... 

Quantum Mechanics theory that explains the behavior of matter using wave functions to characterize the energy of electrons in atoms... 

The key new ideas of qnantnm mechanics include the quantization of energy, a probabilistic description of particle motion, wave-particle duality, and indeterminacy. These ideas appear foreign to ns because they are inconsistent with our experience of the macroscopic world. We have accepted them because they have provided the most comprehensive account of the behavior of matter and radiation and because the agreement between theory and the results of all experiments conducted to date has been astonishingly accurate. 

We believe that such reconciliation Is not adequate. Moreover, we believe that the thermodynamic behavior of matter is due to quantum uncertainties of the same nature but broader than those associated with wave functions and invoked in the uncertainty principle. 

In the present section we shall discuss another aspect of the behavior of matter in an electromagnetic field. We shall analyze by means of statistical-mechanical methods the propagation of electromagnetic waves through a fluid. We shall assume that our system consists of optically isotropic, electrically neutral molecules... 

As you can see from the results of Example 4-7, the particles of the subatomic world behave very differently from the macroscopic objects with which we are familiar. To talk about the behavior of atoms and their particles, we must give up many of our long-held g views about the behavior of matter. We must be willing to visualize a world of new and unfamiliar properties, such as the ability to act in some ways like a particle and in other ways like a wave. 

De Broglie s insight and the Davisson-Germer experiment ultimately pointed out that matter has wave properties. For large pieces of matter, the wave properties can be ignored, but for small pieces of matter like electrons, they cannot be. Because classical mechanics did not consider matter as waves, it was inadequate to describe the behavior of matter. 

Since de Broglie indicated that matter should have wave properties, why not describe the behavior of matter using an expression for a wave The first postulate of quantum mechanics is that the state of a system can be described by an expression called a wavefunction. Wavefunctions in quantum mechanics are typically given the symbol if/ or (the Greek letter psi). For various physical and mathematical reasons, these " P s are limited, or constrained, to being functions that are ... 

All debates on the interpretation of quantum mechanics must end in confusion, unless the classical and non-classical models of the world are clearly distinguished. The classical model is based on the assumption that persistent fragmentation of matter terminates in a set of elementary particles that resist further subdivision, but retain the innate quality to predict the behavior of matter in the bulk. A non-classical alternative starts at the other extreme with a featureless plenum that develops periodic wave structures in a topologically closed universe. In projective relativity [25], there is... 

The most serious setback for a modern theory of matter was the deliberate suppression of Erwin Schrodinger s demonstration that the behavior of electrons in an atom cannot be described correctly by a particle model and quantum jumps [5,6]. A beautiful theory, based on a wave model of matter, was buried through professional rivalry to be replaced by incomprehensible concepts such as particles with wavelike properties—even Zitterbewegung, infinite self-energy, probability density, non-Boolean algebra of observables and other weird properties. Remember how Newton described particles as... 

It has been found that the above theory is quite useful in predicting the correct overall behavior of matter in the presence of electromagnetic radiation. However, in order to predict correctly Raman intensities, it has been found necessary to refine the theory by accounting for small deviations in the electronic wave functions with nuclear motion. In the framework of the Herzberg-Teller theory, it is assumed that the corrected electronic wave functions may be obtained by the use of a first-order perturbation expansion as a linear combination of the complete set of zero-order Born-Oppenheimer functions, discussed above. Since here we are mainly interested in the normal Raman effect, we shall consider only corrections to the second term in Eq. (41). If we first examine corrections to the state X, the resulting expression for the derivative of the transition moment with motion along a normal mode is ... 

Bauer, F. (1982), Behavior of Ferroelectric Ceramics and PVF2 Polymers Under Shock Loading, in Shock Waves in Condensed Matter—1981 (edited by W.J. Nellis, L. Seaman, and R.A. Graham) American Institute of Physics, New York, pp. 251-267. 

Chhabildas, L.C. and D.E. Grady (1984), Shock Loading Behavior of Fused Quartz, in Shock Waves in Condensed Matter—1983 (edited by J.R. Asay, R.A. Graham, and G.K. Straub), Elsevier Science, New York, pp. 175-178. 

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. ... 

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