Quantized phenomena

The idea that energy is quantized rather than continuous may seem strange, but the concept of quantization has many everyday analogies. For example, vending machines dispense cans or bottles of soft drinks only in whole numbers (you can t buy part of a can or bottle from a machine). Each can or bottle is a quantum of its soft drink. Even processes in living systems involve quantized phenomena. The eggs laid by hens are quanta (hens lay only whole eggs). Similarly, when a... 

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... 

The size-dependent properties of nanoparticles differ greatly from the corresponding bulk materials. An example is the size quantization phenomenon commonly observed in II-VI and III-V inorganic semiconductor nanocrystals.6 During the intermediate transition towards that of the bulk metal (usually between 2 and 20 nm), localization of electrons and holes in a confined volume causes an increase in its effective optical band gap as the size of the nanoparticle decreases, observed as a blue shift in its optical spectrum. Bms predicted that there should also be a dependence on the redox potential for these same classes of quantum dots.7 Bard and coworkers showed this experimentally and have reported on the direct observation between the... 

S A discussion of rotation about a double bond on the basis of the quantum mechanics has been published by E. Hiickel, Z. Physik, 60, 423 (1930), which is, I feel, neither so straightforward nor so convincing as the above treatment, inasmuch as neither the phenomenon of concentration of the bond eigenfunctions nor that of change in quantization is taken into account. 

D. V. Averim and K. K. Likharev developed a theory for describing the behavior of small tunneling junctions based on electron interactions. They had started from previous work on Josephson junctions (Likharev and Zorin 1985, Ben-Jacob 1985, Averin and Likharev 1986b) and established the fundamental features of the single-charging phenomena. Their work is based on a quantization theory and handles the tunneling phenomenon as a perturbation, described by annihilation and creation operators of a Hamiltonian. 

Photoelectric effect The effect produced when electromagnetic radiation knocks electrons out of a metal. Einstein used this phenomenon to show that light was quantized and came in energy packets called photons. 

Transition state theory, as embodied in Eq. 10.3, or implicitly in Arrhenius theory, is inherently semiclassical. Quantum mechanics plays a role only in consideration of the quantized nature of molecular vibrations, etc., in a statistical fashion. But, a critical assumption is that only those molecules with energies exceeding that of the transition state barrier may undergo reaction. In reality, however, the quantum nature of the nuclei themselves permits reaction by some fraction of molecules possessing less than the energy required to surmount the barrier. This phenomenon forms the basis for QMT. ... 

This source of noise is not usually called noise in most technical contexts it is more commonly called error rather than noise, but that is just a label since it is a random contribution to the measured signal, it qualifies as noise just as much as any other noise source. So what is this mystery phenomenon It is the quantization noise introduced by the analog-to-digital (A/D) conversion process, and is engendered by the fact that for... 

In fact, electron transfer occurs at the microscopic level where quantum mechanics provides the necessary description of the phenomenon (5-13). In the quantum mechanical solution, associated with the potential curves in Figure 1 are quantized energy levels, Ej = (vj + 1/2) 100., where Vj and 2ttvj are the vibrational... 

The main goal of this report is to present a phenomenon of highly general nature manifested in various dynamical systems. We present the occurrence of peculiar quantization by the parameter of intensity of the excited oscillations and we show that given unchanging conditions it is possible to excite oscillations with a strictly defined discrete set of amplitudes the rest of the amplitudes being forbidden . The realization of oscillations with a specific amplitude from the permitted discrete set of amplitudes is determined by the initial conditions. The occurrence of this unusual property is predetermined by the new general initial conditions, i.e. the nonlinear action of the external excited force with respect to the coordinate of the system subjected to excitation. 

Quantization (the idea of quantums, photons, phonons, gravitons) is postulated in Quantum Mechanics, while the Theory of Relativity does not derive quantization from geometric considerations. In the case of the established phenomenon the quantized nature of portioned energy transfer stems directly from the mechanisms of the process and has a precise mathematical description. The quasi-harmonic oscillator obeys the classical laws to a greater extent than any other system. A number of problems, related to quasi-harmonic oscillators, have the same solution in classical and quantum mechanics. 

Damgov, V. and Trenchev PI. Phenomenon of Quantized Oscillation Excitation. Nonlinearity and Disorder Theory and Applications, F.Abdulaev et al. (Eds), Kluwer Academic Publishers, Netherlends, P. 397 (2001)... 

Hertz s experiment as being caused by electrons [2], The phenomenon of photoemission has played an important role in confirming Einstein s famous postulate, published in 1905, that light is quantized in photons of energy hv[3J. We refer to Margaritondo [4] for an interesting review on the early days of the photoelectric effect. 

When the lamellae are annealed at a given temperature, they thicken with time. The thickening is usually continuous and L increases logarithmically with time. However, there are several examples, where the lamellar thickness increases in a stepwise manner. For example, the initial lamella may contain chains each with four folds (five stems). As thickening process continues, the lamellar thickness jumps discontinuously to three folds, and so on. This phenomenon is referred to as quantized thickening [25]. 

The magnetic field quantizes the motion of the quasi-particles in the plane perpendicular to the resulting levels are known as Landau levels, and the phenomenon is... 

The detection of sharp plasmon absorption signifies the onset of metallic character. This phenomenon occurs in the presence of a conduction band intersected by the Fermi level, which enables electron-hole pairs of all energies, no matter how small, to be excited. A metal, of course, conducts current electrically and its resistivity has a positive temperature coefficient. On the basis of these definitions, aqueous 5-10 nm colloidal silver particles, in the millimolar concentration range, can be considered to be metallic. Smaller particles in the 100-A > D > 20-A size domain, which exhibit absorption spectra blue-shifted from the plasmon band (Fig. 80), have been suggested to be quasi-metallic [513] these particles are size-quantized [8-11]. Still smaller particles, having distinct absorption bands in the ultraviolet region, are non-metallic silver clusters. 

As the twentieth century progressed, it became increasingly clear that quantization was not only a characteristic of light, but also of the fundamental particles from which matter is constructed. Bound electrons in atoms, in particular, are clearly limited to discrete energies (levels) as indicated by their ultraviolet and visible line spectra. This phenomenon has no classical correspondence - in a classical system, obeying Newtonian mechanics, energy can vary continuously. 

In conclusion, quantum dynamical localization plays an important role in the excitation and ionization process of atoms and molecules. A question that remains open in connection with the previous talk is whether quantization via periodic orbits can account for this phenomenon. 

All the phenomena described above are absent in a 2D-junction when the effects of transverse mode quantization are neglected [7]. We have considered the limiting case of a single (transverse) channel because this is the case when the effects induced by a dispersion asymmetry in the electron spectrum are most pronounced. The anomalous supercurrent Eq. (7) is a sign alternating function of the transverse channel index since for neighboring channels the spin projections of chiral states are opposite [4]. Besides, the absolute value of the dispersion asymmetry parameter decreases with transverse-channel number j. So, for a multichannel junction the effects related to a dispersion asymmetry phenomenon will be strongly suppressed and they completely disappear in the pure 2D case. 

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