General Quantum-mechanical Description Research Articles

Quantum-mechanical description of spin 1/2 particles and nuclei channeled in bent crystals

General quantum-mechanical description of relativistic particles and nuclei with spin 1/2 channeled in bent crystals is performed with the use of the cylindrical coordinate system. The previously derived Dirac equation in this system is added by terms characterizing anomalous magnetic and electric dipole moments. A transformation to the Foldy-Wouthuysen representation, a derivation of the quantum-mechanical equations of motion for particles and their spins, and a determination of classical limit of these equations are fulfilled in the general case. A physical nature of main peculiarities of description of particles and nuclei in the cylindrical coordinate system is ascertained.

Determination of theGe-nanocrystal/SiO2matrix interface trap density from the small signal response of charge stored in the nanocrystals

We investigate the linear response of charge stored in Ge nanocrystals (NCs) embedded in ${\text{SiO}}_{2}$ to an alternating electric field in order to study the electronic properties of the $\text{Ge-NC}/{\text{SiO}}_{2}$ interface. Experimentally, the modulation of the cluster charge is sensed by the transient drain current of field-effect transistors in whose gate oxide the nanocrystals are embedded. For interpretation of the experimental results, we present a small-signal model obtained from a first-order expansion of the general quantum-mechanical description of the system. The contribution of trap states to the alternation of the cluster charge is distinguished from that of quantized states in the NC conduction band by calculating the latter one by density functional theory and subtracting it from the experimental values. A high $\text{Ge-NC}/{\text{SiO}}_{2}$ interface density of $2.8\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }{\text{cm}}^{\ensuremath{-}2}\text{ }{\text{eV}}^{\ensuremath{-}1}$ is obtained. These traps cannot be passivated efficiently by a hydrogen anneal at $450\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$ and mediate efficient nonradiative recombination processes.

Interaction of Single Molecules With Metallic Nanoparticles

We theoretically investigate the interaction between a single molecule and a metallic nanoparticle (MNP). We develop a general quantum mechanical description for the calculation of the enhancement of radiative and nonradiative decay channels for a molecule situated in the near-field regime of the MNP. Using a boundary element method approach, we compute the scattering rates for several nanoparticle shapes. We also introduce an eigenmode expansion and quantization scheme for the surface plasmons, which allows us to analyze the scattering processes in simple physical terms. An intuitive explanation is given for the large quantum yield of quasi-1-D and quasi-2-D nanostructures. Finally, we briefly discuss resonant Forster energy transfer in presence of MNPs.

Origin of mutual exclusiveness in Bohr’s complementarity principle

According to Bohr’s complementarity principle, two distinct types of complementarity exist-one of complementary variables and other in the so-called wave-particle complementarity experiments. Some authors have claimed that mutual exclusiveness (ME) in both the cases arise due to uncertainty principle and have analysed the second type in terms of Fourier space analysis and consequent putative “momentum kick” distribution. Some others, on the other hand, have identified the collapse hypothesis as the actual quantum mechanical principle responsible for ME in the interferometry experiments. In this paper the momentum space analysis is thoroughly examined vis-a-vis the general quantum mechanical description in terms of the changes in the wave function. It is argued that such alternative explanations are not in full conformity with the strict quantum mechanical description.

Symmetry, relativity and quantum mechanics

The objective is to investigate the physical meaning of a quantum property-as yet unnoticed-stated as «homogeneity of statistical ensembles», which, together with the hypotheses of statistical determinism and of invariance of the formal structure under some group of transformations, allows in a direct way to deduce the most general quantum-mechanical description in terms of density operators written as linear combinations of irreducible polarization tensors, a decomposition which plays a considerable role in quantum optics and collision theory. The hypothesis of invariance is analogous to the relativity principle, and the theory of quantum kinetic momentum is recovered in the special case of spherical symmetry, without additional assumptions. Thus these hypotheses give the physical meaning of the density-matrix formalism, which is derived as a direct theory of quantum probabilities, dispensing with the usual postulates concerning amplitudes. As a contribution to the interpretation debate of quantum theory, it is suggested that the polarization tensors should be considered as «new elements of physical reality» which cannot be ruled out by the Greenberger-Horne-Zeilinger argument or its future extensions.

Quantum Transport in Thin-Film Structures

Transport in thin-film structures (single films and multilayers) is of current interest [1-4] due to new interesting phenomena found in such systems. Quasiclassical description based on the Boltzmann transport equation is very often applied to such structures, however, it underestimates the electron scattering by surfaces and/or interfaces. In this paper we formulate a general quantum mechanical description of electronic transport in thin-film structures. The approach is based on the single electron transport theory which was applied to many problems like weak localization, universal conductance fluctuations etc. [5]. The main contribution to the global in-plane conductivity is given, for each spin direction, by the formula

Free-electron lasers: Amplification, multiphoton transitions, saturation, and geometry

A review of the literature and the main ideas on free-electron lasers (FEL's) is presented. Various approaches to describe the physical processes in FEL's are discussed. With the aid of a general quantum-mechanical description, the probabilities of multiphoton transitions in FEL's are found. Typically, the number of photons that are absorbed or emitted in FEL's is large even in a very weak field. Nevertheless, over a wide range of parameters the gain coefficient in the FEL coincides with that derived in the weak-field approximation. At the strong-field limit, an analytical expression for the saturated gain is found using either a quantum-mechanical or classical approach. The possibility of optimizing the gain in the Compton laser is discussed; this optimization is connected with use of a noncolinear scattering scheme for electron beams with a rather large energy spread.

The effect of intramolecular quantum modes on free energy relationships for electron transfer reactions

A general quantum mechanical description of exothermic electron transfer reactions is formulated by treating such reactions as the nonradiative decay of a ’’supermolecule’’ consisting of the electron donor, the electron acceptor, and the polar solvent. In particular, the role of the high-frequency intramolecular degrees of feedom on the free energy relationship for series of closely related reactions was investigated for various model systems involving displacement of potential energy surfaces, frequency shift, and anharmonicity effects. The free energy plots are generally found to pass through a maximum and to be asymmetric with a slower decrease in the transition probability with increasing energy of reaction. For high-frequency intramolecular modes this provides a rationalization of the experimental observation of ’’activationless’’ regions. Isotope effects are discussed as also are the oscillatory free energy relationships, predicted for low temperatures and high frequencies, and which are analogous to the vibrational structure in optical transitions.