Energy wave-particle duality

Quantum mechanics deals with the mathematical description of the motion and interaction of sub-atomic particles, incorporating the concepts of quantization of energy, wave—particle duality, the uncertainty principle, and the correspondence principle. 

If we think in terms of the particulate nature of light (wave-particle duality), the number of particles of light or other electi omagnetic radiation (photons) in a unit of frequency space constitutes a number density. The blackbody radiation curve in Fig. 1-1, a plot of radiation energy density p on the vertical axis as a function of frequency v on the horizontal axis, is essentially a plot of the number densities of light particles in small intervals of frequency space. 

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... 

How do we understand and describe this wave-particle duality Clearly a plane wave, A exp[i(kx - cot)], has a well-defined angular frequency, (or energy), and wave vector, (or momentum). But it is infinite in extent, with its intensity, A 2, being uniform everywhere in space. In order to create a localized disturbance we must form a wave packet by superposing plane waves of different wavevectors. Mathematically this is written... 

In classical mechanics, Newton s laws of motion determine the path or time evolution of a particle of mass, m. In quantum mechanics what is the corresponding equation that governs the time evolution of the wave function, F(r, t) Obviously this equation cannot be obtained from classical physics. However, it can be derived using a plausibility argument that is centred on the principle of wave-particle duality. Consider first the case of a free particle travelling in one dimension on which no forces act, that is, it moves in a region of constant potential, V. Then by the conservation of energy... 

Wave-particle duality does / V I not mean that energy is... 

The first inference of photon mass was made by Einstein and de Broglie on the assumption that the photon is a particle, and behaves as a particle in, for example, the Compton and photoelectric effects. The wave-particle duality of de Broglie is essentially an extension of the photon, as the quantum of energy, to the photon, as a particle with quantized momentum. The Beth experiment in 1936 showed that the photon has angular momentum, whose quantum is h. Other fundamental quanta of the photon are inferred in Ref. 42. In 1930, Proca [43] extended the Maxwell-Heaviside theory using the de Broglie guidance theorem ... 

Quantum of radiation) An elementary particle of electromagnetic energy in the sense of the wave-particle duality. 

The thermal conductivity of a metal or alloy consists of two components, a phonon contribution (a phonon is a quantum of acoustic energy, which possesses wave-particle duality), Kph, and an electronic contribution (free electrons moving through the crystal also carry thermal energy), k i- In pure metals, Xei is the dominant contribution to the total thermal conduction. This free electron contribution to the thermal conductivity is given by the gas-kinetic formula as ... 

The series of Radioactive disintegrations the uranium-radium series, the uranium-actinium series, the thorium series, and the neptunium series. The age of the earth. The fundamental particles electron, proton, positron, neutron, positive, negative, and neutral mesons, neutrino. The photon (light quantum) the energy of a photon, hv. Planck s constant. The wave-particle duality of light and of matter. The wavelengths of electrons. 

The conventional macroscopic Fourier conduction model violates this non-local feature of microscale heat transfer, and alternative approaches are necessary for analysis. The most suitable model to date is the concept of phonon. The thermal energy in a uniform solid material can be jntetpreied as the vibrations of a regular lattice of closely bound atoms inside. These atoms exhibit collective modes of sound waves (phonons) wliich transports energy at tlie speed of sound in a material. Following quantum mechanical principles, phonons exhibit paiticle-like properties of bosons with zero spin (wave-particle duality). Phonons play an important role in many of the physical properties of solids, such as the thermal and the electrical conductivities. In insulating solids, phonons are also (he primary mechanism by which heal conduction takes place. 

Equation (1.5) establishes a bridge between a description of fight as an (electromagnetic) wave of frequency v and as a beam of -q energy particles. If phenomena related to time averages, such as diffraction and interference, can be easily interpreted in terms of waves, other phenomena, involving a one-to-one relation such as the photoelectric and the Compton effects, require a description based on corpuscular attributes. This wave-particle duality reflects the use of one or the other description depending on the experiment performed, while no experiment exists which exhibits both aspects of the duality simultaneously. 

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. 

Wave-particle duality accounts for the probabilistic nature of quantum mechanics and for indeterminacy. Once we accept that particles can behave as waves, then we can apply the resnlts of classical electromagnetic theory to particles. By analogy, the probability is the sqnare of the amplitnde. Zero-point energy is a con-seqnence of the Heisenberg nncertainty relation all particles bound in potential wells have finite energy even at the absolnte zero of temperature. 

Max Planck noted that in certain situations, energy possessed particlelike properties. A French physicist, Louis deBroglie, hypothesized that the reverse could be true as well Electrons could, at times, behave as waves rather than particles. This is known today as deBroglie s wave-particle duality. 

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