scholarly journals The quantum theory and the dielectric constant

1924 ◽  
Vol 105 (734) ◽  
pp. 650-661 ◽  
Keyword(s):  
Dielectric Constant ◽  
Quantum Theory ◽  
Electric Field ◽  
Total Energy ◽  
Quantum Number ◽  
Quantum Numbers

The change of energy of an atom of hydrogen when submitted to an electric field has been calculated by Epstein. If W denotes the total energy of an atom, then the change in energy Δ W, due to the field F, is given by ΔW = - 3 h 2 F/8 π 2 m E ( n 2 - n 1 ) ( n 1 + n 2 + n 3 ) + 17 e 2 F 2 /(16 π R H ) 2 m Z ( n 1 , n 2 , n 3 ), where R H is Rydberg's constant for hydrogen and Z ( n 1 , n 2 , n 3 ) = ( n 1 + n 2 + n 3 ) 6 {1 - 3/17 ( n 1 - n 2 /( n 1 + n 2 + n 3 ) 2 - 9/17 ( n 3 / n 1 + n 2 + n 3 ) 2 }, and n 1 and n 2 are parabolic quantum numbers and n 3 is the equatorial quantum number.

III.—Observations on the Balmer Series of Hydrogen

1925 ◽  
Vol 44 ◽  
pp. 14-20
Author(s):  
A. E. M. Geddes
Keyword(s):  
Quantum Theory ◽  
Total Energy ◽  
The Other ◽  
Elliptical Orbit ◽  
Balmer Series ◽  
Quantum Numbers ◽  
Image Position

According to the quantum theory of the production of spectra the lines Hα and Hβ of the Balmer series in the hydrogen spectrum may be produced in six and eight different ways respectively. This general conclusion, however, has to be modified. The mass of an electron in its elliptical orbit is not constant but depends upon its velocity. Consequently, the total energy of an electron in its orbit must be expressed in the formwhere na and nr are the azimuthal and radial quantum numbers and where , and the other symbols have their usual meaning.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

The Hertzian Spectrum of Rubber and Its Micellar Constitution

1946 ◽  
Vol 19 (4) ◽  
pp. 1085-1087
Author(s):  
Pierre Girard ◽  
Paul Abadie
Keyword(s):  
Dielectric Constant ◽  
Electric Field ◽  
Wave Length ◽  
Structural Features ◽  
Loss Angle ◽  
First Case ◽  
Dipolar Molecules ◽  
Alternating Electric Field ◽  
Different Types ◽  
Absorption And Dispersion

Abstract The spectra which were studied lie within the region of hertzian frequencies, and can be represented either by dispersion curves showing the dielectric constant of the substance as a function of the frequency (or wave length λ), or by absorption curves showing the loss angle as a function of this frequency. These two types of curves represent the same phenomenon, i.e., orientation of the dipolar molecules in the alternating electric field, in accordance with the theory of Debye. The spectra and their interpretation depend chiefly on whether the molecules are crystalloid with relatively small and similar dimensions, or are colloidal, with large and unequal dimensions. In the first case, the spectra gives evidence chiefly on the form of the molecules and their structural features. Dilution in a nonpolar solvent shows for certain dipolar compounds, e.g., alcohol, considerable deformations, which differ according to the solvent. In the case of colloids, e.g., rubber, which has a permanent moment, the spectra and the meaning of these spectra are far different. In this case the spectra indicate that the absorption and dispersion values in the hertzian region are closely related to the micellar constitution, i.e., to the different types of micelles, to their size, and to the proportion of each type.

scholarly journals F-centers mechanism of long-term relaxation in lead zirconate-titanate based piezoelectric ceramics. 2. After-field relaxation

2016 ◽  
Vol 06 (03) ◽  
pp. 1650019 ◽  
Author(s):  
V. M. Ishchuk ◽  
D. V. Kuzenko
Keyword(s):  
Dielectric Constant ◽  
Electric Field ◽  
Lead Zirconate Titanate ◽  
Oxygen Vacancies ◽  
Lead Zirconate ◽  
Relaxation Processes ◽  
Logarithmic Function ◽  
External Effects ◽  
Dc Electric Field

The paper presents results of experimental study of the dielectric constant relaxation during aging process in Pb(Zr,Ti)O3based solid solutions (PZT) after action of external DC electric field. The said process is a long-term one and is described by the logarithmic function of time. Reversible and nonreversible relaxation process takes place depending on the field intensity. The relaxation rate depends on the field strength also, and the said dependence has nonlinear and nonmonotonic form, if external field leads to domain disordering. The oxygen vacancies-based model for description of the long-term relaxation processes is suggested. The model takes into account the oxygen vacancies on the sample's surface ends, their conversion into [Formula: see text]- and [Formula: see text]-centers under external effects and subsequent relaxation of these centers into the simple oxygen vacancies after the action termination. [Formula: see text]-centers formation leads to the violation of the original sample's electroneutrality, and generate intrinsic DC electric field into the sample. Relaxation of [Formula: see text]-centers is accompanied by the reduction of the electric field, induced by them, and relaxation of the dielectric constant, as consequent effect.

scholarly journals Поведение керамических твердых растворов 33PbYb-=SUB=-1/2-=/SUB=-Nb-=SUB=-1/2-=/SUB=-O-=SUB=-3-=/SUB=--22PbZrO-=SUB=-3-=/SUB=--45PbTiO-=SUB=-3-=/SUB=- в электрическом поле

2020 ◽  
Vol 46 (6) ◽  
pp. 31
Author(s):  
Л.С. Камзина ◽  
G. Li
Keyword(s):  
Phase Transition ◽  
Dielectric Constant ◽  
Electric Field ◽  
Electric Fields ◽  
Dielectric Parameters ◽  
Morphotropic Phase Transition ◽  
Temperature Dependences ◽  
Pseudocubic Phase

The temperature dependences of the dielectric parameters were studied, as well as the changes in the dielectric constant with time in ceramic 33PbYb1 / 2Nb1 / 2O3-22PbZrO3-45 PbTiO3 samples in electric fields (0 <E <8 kV / cm). It is shown that in the phase existing below the temperature of the morphotropic phase transition, in addition to the rhombohedral and tetragonal phases, a small fraction of the relaxor pseudocubic phase is present. It was found that, unlike other relaxors, the dielectric constant practically does not change with time when an electric field is applied in the phase below the temperature of the morphotropic phase transition. Possible reasons for this behavior are discussed.

scholarly journals Space Charge and Electric Field Analysis on Contaminated XLPE Insulator

2018 ◽  
Vol 12 (1) ◽  
pp. 370
Author(s):  
M.H.A. Wahab ◽  
N. A. M. Jamail ◽  
E. Sulaiman ◽  
Q.E. Kamarudin ◽  
N.A. Othman ◽  
...  
Keyword(s):  
Dielectric Constant ◽  
Electric Field ◽  
Space Charge ◽  
Dielectric Strength ◽  
Field Analysis ◽  
Ethylene Dichloride ◽  
Xlpe Cable ◽  
Lower Dielectric Constant ◽  
High Dielectric ◽  
Xlpe Insulation

<p>Nowadays, XLPE cable has been widely used because it has better resistance than other cables. XLPE insulation has unique features including a high dielectric strength and high insulation resistance. A lot of researches based on hardware and software have been conducted to prove the effectiveness of XLPE cable such as AC and DC applications and Space Charge Distribution measurement under HVDC at High Temperature. This research focused on analysis of space charge and electric field on XLPE cable with effect of non-uniform contamination layer by using Quickfield Software. Non-uniform contaminations have been applied along XLPE cable using Arsenic Tribromide (AsBr3), Boron Bromide (BBr3), Ethylene Dichloride (CH2C1), Formic Acid (CH1O2), Formamide (CH3NO) and Alcohol element. Presence of these contamination elements represent of underground contamination. The size and layer of the contamination were non-uniform type. From the results, it is shown that lower dielectric constant of contamination will affect more on charge of XLPE insulation. As a conclusion, it can be seen lower dielectric constant value of contamination element greatly affecting the performance of XLPE insulation. Furthermore, size of contamination also influences the content of charge in contamination where the bigger the contamination size, the more charge contained in the contamination.</p>

scholarly journals Improve the Hole Size-dependent Refractive Index Sensitivity  of Au-Ag Nanocages by Tuning the Alloy Composition

2021 ◽  
Author(s):  
Jianjun LI ◽  
Qiu-Xiang Qin ◽  
Guo-Jun Weng ◽  
Jian Zhu ◽  
Jun-Wu Zhao
Keyword(s):  
Dielectric Constant ◽  
Refractive Index ◽  
Electric Field ◽  
Alloy Composition ◽  
Geometric Parameters ◽  
Sensitivity Factor ◽  
Hole Size ◽  
Refractive Index Sensitivity ◽  
Electric Field Direction ◽  
Index Sensitivity

Abstract In this study, the nanoboxes is converted into Au-Ag alloy nanocages by increasing the hole size. Discrete dipole approximation (DDA) is used to study the extinction spectrum and the refractive index sensing characteristics of Au-Ag alloy nanocages with different geometric parameters. With the increase of Au component, the local surface plasmon resonance (LSPR) peak shows approximately linear redshift and the sensitivity factor shows approximately linear decrease. The refractive index sensitivity can be effectively controlled by the Au-Ag ratio at large hole size because the hole and cavity surfaces distribute more environmental dielectric components. Therefore, increasing the hole size and decreasing the Au-Ag ratio can improve the refractive index sensitivity. To explain the effect of alloy composition on the LSPR characteristics and the refractive index sensitivity, the local electric field distributions with different geometric parameters are plotted. We find that the electric field direction on the hole and cavity surfaces are controlled by the Au-Ag ratio and environmental dielectric constant. Moreover, the field vector on the hole and cavity surfaces are formed by the superposition of the incident field, the electric field generated by the oscillating electrons on the outer surface, and the polarized field in the environmental dielectric constant.

scholarly journals Radiation Pattern Reconfigurable Waveguide Slot Array Antenna Using Liquid Crystal

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Hongyu Shi ◽  
Jianxing Li ◽  
Shitao Zhu ◽  
Anxue Zhang ◽  
Zhuo Xu
Keyword(s):  
Dielectric Constant ◽  
Liquid Crystal ◽  
Electric Field ◽  
Radiation Pattern ◽  
Array Antenna ◽  
Antenna Element ◽  
Waveguide Slot ◽  
Radiation Direction ◽  
Coupled Resonator

In this paper, we proposed a radiation pattern reconfigurable waveguide slot array antenna using liquid crystal (LC). Together with the waveguide slot, the designed complementary electric-field-coupled resonator functions like a switch controlled by the dielectric constant of the LC, which can control the antenna element to radiate or not. Thus, the array factor and radiation pattern can be manipulated. The proposed antenna was simulated, fabricated, and measured. Its radiation direction can be reconfigured to 46° or 0° at about 15 GHz.

Research on Electric Field Simulation of Ring Capacitance Sensor Based on Finite Element Method

2021 ◽  
Vol 105 ◽  
pp. 221-227
Author(s):  
Hui Ling Wang ◽  
Chun Li Cai
Keyword(s):  
Dielectric Constant ◽  
Finite Element ◽  
Electric Field ◽  
Field Intensity ◽  
Electric Field Intensity ◽  
Element Model ◽  
Field Analysis ◽  
Optimal Structure ◽  
Capacitance Sensor ◽  
Finite Element Software

The working principle of ring capacitance sensor is introduced, that is capacitance fringe effect. Finite element model is established through the Hybrid-Trefftz algorithm. Electric field analysis and simulation calculation of different sensor model are done with the finite element software ANSYS, and the optimal structure combination is obtained. And followed the example of optimal structure, the relation of dielectric constant and electric field intensity were given. The result of simulation shows the most direct and the most important two parameters that affect the sensor performance in the design of the ring capacitance sensor are the two electrodes spacing and the length. The dielectric constant of measured medium is smaller, the intensity of electric field intensity is greater. The simulation for subsequent product design has a good theoretical guidance.

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