Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transform...Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.展开更多
The quantum electrodynamic (QED) behaviour is studied for quantum Hall effect (QHE). Quantum theory with conjecture of fractional charge quantization (quantum dipole moment), eigenfunctions for fractional charge quant...The quantum electrodynamic (QED) behaviour is studied for quantum Hall effect (QHE). Quantum theory with conjecture of fractional charge quantization (quantum dipole moment), eigenfunctions for fractional charge quantization at the surface of a twisted and twigged electron quanta and above its surface, fractional Fourier transform and Hermite function for fractional charge quantization is developed. With energy eigen value equation for QHE and with energy operator on an eigenfunction of a twisted and twigged electron quanta, the corresponding eigenfunctions are normalized with Schrodinger’s quantum wave mechanical equation for electric scalar and magnetic potentials, respectively (QED behavior). The fractional electric and magnetic fields with their corresponding potentials for the quantized fractional states in semiconducting hereto structures are theoretically calculated. Such mathematical expressions are in good agreement with experimental results of Nobel Prize winning scientists Klitzing, Haroche, Peter and Gruebber. Our results can also explain the hybridized states of orbits with emphasis on sigma and pi bonding and their corresponding antibonding orbitals as a manifestation of electrophilic and nucleophilic chemical reactions.展开更多
The wavelet transformation is applied to the high current transformer.The high current transformer elaborated in the paper is mainly applied to the measurement of AC/DC high current.The principle of the transformer is...The wavelet transformation is applied to the high current transformer.The high current transformer elaborated in the paper is mainly applied to the measurement of AC/DC high current.The principle of the transformer is the Hall direct measurement principle.The transformer has the following three characteristics:firstly, the effect of the remnant field of the iron core on the measurement is decreased;secondly,because the temperature compensation is adopted,the transformer has good temperature charactreristic;thirdly,be cause the wavelet transfomation technology is adopted,the transformer has the capacity of good antijanming.展开更多
This study focuses on the combined impact of heat source/sink and chemical reaction on slip flow of micropolar fluid through a permeable wedge in the existence of Hall and ion-slip currents.The governing highly non-li...This study focuses on the combined impact of heat source/sink and chemical reaction on slip flow of micropolar fluid through a permeable wedge in the existence of Hall and ion-slip currents.The governing highly non-lincar PDEs were altered into a set of non-linear coupled ODEs by using similarity transformations.Differential transformation method(DTM)has been implemented in transformed ODEs equations.The comparison with previous literatures was performed and the data of this study was found to be in accordance with each other.The analytical solutions for skin-friction coefficients(surface drag forces),Nussclt and Sherwood numbers are depicted through graphs and tables.The study of boundary layer flow over a wedge surface plays an imperative role in the field of aerodynamics,heat exchanger,ground water pollution and geothermal system etc.展开更多
文摘Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.
文摘The quantum electrodynamic (QED) behaviour is studied for quantum Hall effect (QHE). Quantum theory with conjecture of fractional charge quantization (quantum dipole moment), eigenfunctions for fractional charge quantization at the surface of a twisted and twigged electron quanta and above its surface, fractional Fourier transform and Hermite function for fractional charge quantization is developed. With energy eigen value equation for QHE and with energy operator on an eigenfunction of a twisted and twigged electron quanta, the corresponding eigenfunctions are normalized with Schrodinger’s quantum wave mechanical equation for electric scalar and magnetic potentials, respectively (QED behavior). The fractional electric and magnetic fields with their corresponding potentials for the quantized fractional states in semiconducting hereto structures are theoretically calculated. Such mathematical expressions are in good agreement with experimental results of Nobel Prize winning scientists Klitzing, Haroche, Peter and Gruebber. Our results can also explain the hybridized states of orbits with emphasis on sigma and pi bonding and their corresponding antibonding orbitals as a manifestation of electrophilic and nucleophilic chemical reactions.
基金ThispaperissupportedbyNationalNatureScienceFoundationofChina (No 60 1760 2 0 )
文摘The wavelet transformation is applied to the high current transformer.The high current transformer elaborated in the paper is mainly applied to the measurement of AC/DC high current.The principle of the transformer is the Hall direct measurement principle.The transformer has the following three characteristics:firstly, the effect of the remnant field of the iron core on the measurement is decreased;secondly,because the temperature compensation is adopted,the transformer has good temperature charactreristic;thirdly,be cause the wavelet transfomation technology is adopted,the transformer has the capacity of good antijanming.
文摘This study focuses on the combined impact of heat source/sink and chemical reaction on slip flow of micropolar fluid through a permeable wedge in the existence of Hall and ion-slip currents.The governing highly non-lincar PDEs were altered into a set of non-linear coupled ODEs by using similarity transformations.Differential transformation method(DTM)has been implemented in transformed ODEs equations.The comparison with previous literatures was performed and the data of this study was found to be in accordance with each other.The analytical solutions for skin-friction coefficients(surface drag forces),Nussclt and Sherwood numbers are depicted through graphs and tables.The study of boundary layer flow over a wedge surface plays an imperative role in the field of aerodynamics,heat exchanger,ground water pollution and geothermal system etc.
