Photon Structure and Wave Function from the Vector Potential Quantization

A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.

MHD Equilibrium with Reversed Current Density and Magnetic Islands Revisited:the Vacuum Vector Potential Calculus

The solution of Grad-Shafranov equation determines the stationary behavior of fusion plasma inside a tokamak. To solve the equation it is necessary to know the toroidal current density profile. Recent works show that it is possible to determine a magnetohydrodynamic （MHD） equilibrium with reversed current density （RCD） profiles that presents magnetic islands. In this work we show analytical MHD equilibrium with a RCD profile and analyze the structure of the vacuum vector potential associated with these equilibria using the virtual casing principle.

Gradient Transformation of Momentum and Single-Valued Vector Potential in Nonrelativistic Dynamics

A vector potential of a magnetic field in Lagrangian is defined as the necessary partial solution of a inhomogeneous differential equation. The ＂gradient transformation＂ is an addition of arbitrary general solution of the corresponding homogeneous equation that does not change the Lagrange equations. When dynamics is described by momenta and coordinates, this transformation is not the vector potential modification, which does not change expressions for other physical quantities, but a canonical transformation of momentum, which changes expressions for all fimctions of momentum, not changing the Poisson brackets, and, hence, the integrals of motion. The generating function of this transformation must reverse sign under the time-charge reversal. In quantum mechanics the unitary transformation corresponds to this canonical transformation. It also does not change the commutation relations. The phase of this unitary operator also must reverse sign under the time-charge reversal. Examples of necessary vector potentials for some magnetic fields are presented.

The Aharonov-Bohm Effect: An Exploration of Quantum Interference and Electromagnetic Potentials

The AB(Aharonov-Bohm)effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle’s wave function,even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect,an electron beam is split into two paths,with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams,the vector potential A associated with the magnetic flux Φ through the solenoid induces a phase shift in the electron’s wave function.This phase shift,quantified by △φ=qΦ/hc,manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED(quantum electrodynamics),where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems,beyond its classical role.This article outlines the AB effect,including its theoretical framework,experimental observations,and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.

Supersymmetry and Solution of Dirac Equation with Vector and Scalar Potentials

The Dirac equations with vector and scalar potentials of the Coulomb types in two and three dimensions are solved using the supersymmetric quantum mechanics method. For the system of such potentials, the analytical expressions of the matrix dements for both position and momentum operators are obtained.

Electronic Energy Band and Transport Properties in Monolayer Graphene with Periodically Modulated Magnetic Vector Potential and Electrostatic Potential

We investigated the electronic energy band and transport features of graphene superlattice with periodically modulated magnetic vector potential and electrostatic potential. It is found that both parallel magnetic vector potential and electrostatic potential can decisively shift Dirac point in a different way, which may be an efficient way to achieve electron or hole filter. We a/so find that applying modulated parallel and anti-parallel magnetic vector potential to the electrons can efficiently change electronic states between pass and stop states, which can be useful in designing electron or hole switches and lead to large magneto-resistance.

Moist Potential Vorticity Vector for Diagnosis of Heavy Rainfall Events in Tanzania

In this paper, we modify the convective vorticity vector (CVV) defined as a cross product of absolute vorticity and gradient of equivalent potential temperature to moist potential vorticity vector (MPVV) defined as a cross product of absolute vorticity () and the gradient of the moist-air entropy potential temperature (). The patterns of (MPVV) are compared with the patterns of heavy rainfall events that occurred over different regions in Tanzania on 20th to 22nd December, 2011 and on 5th to 8th May, 2015. Moreover, the article aimed at assessing the relative contributions of the magnitude, horizontal and vertical components of (MPVV) detecting on the observed patterns of rainfall events. Dynamic and thermodynamic variables: wind speed, temperature, atmospheric pressure and relative humidity from numerical output generated by the Weather Research and Forecasting (WRF) model running at Tanzania Meteorological Agency (TMA) were used to compute MPVV. It is found that MPVV provide accurate tracking of locations received heavy rainfall, suggesting its potential use as a dynamic tracer for heavy rainfall events in Tanzania. Finally it is found that the first and second components of MPVV contribute almost equally in tracing locations received heavy rainfall events. The magnitude of MPVV described the locations received heavy rainfall events better than the components.

Pulsed Vector Magnetic Potential Field Existence

Experimental confirmation discussed the effect of the immediate surroundings of a pulse-powered toroidal coil on biological material which was placed in an environment without the influence of electromagnetic force.

Approximate solution of the spin-one Duffin-Kemmer-Petiau(DKP) equation under a non-minimal vector Yukawa potential in(1+1)-dimensions

We solve the Duffin-Kemmer-Petiau （DKP） equation with a non-minimal vector Yukawa potential in （1＋1）- dimensional spa^e-time for spin-1 particles. The Nikiforov Uvarov method is used in the calculations, and the eigen- functions as well as the energy eigenvalues are obtained in a proper Pekeris-type approximation.

Exact Solutions of the Klein-Gordon Equation with a New Anharmonic Oscillator Potential

We solve the Klein-Cordon equation with a new anharmonic oscillator potential and present the exact solutions. It is shown that under the condition of equal scalar and vector potentials, the Klein-Cordon equation could be separated into an angular equation and a radial equation. The angular solutions are the associated-Legendre polynomial and the radial solutions are expressed in terms of the confluent hypergeometric functions. Finally, the energy equation is obtained from the boundary condition satisfied by the radial wavefunctions.

Thermochemical Nonequilibrium 2D Modeling of Nitrogen Inductively Coupled Plasma Flow

Two-dimensional（2D） numerical simulations of thermochemical nonequilibrium inductively coupled plasma（ICP） flows inside a 10-kW inductively coupled plasma wind tunnel（ICPWT） were carried out with nitrogen as the working gas.Compressible axisymmetric NavierStokes（N-S） equations coupled with magnetic vector potential equations were solved.A fourtemperature model including an improved electron-vibration relaxation time was used to model the internal energy exchange between electron and heavy particles.The third-order accuracy electron transport properties（3rd AETP） were applied to the simulations.A hybrid chemical kinetic model was adopted to model the chemical nonequilibrium process.The flow characteristics such as thermal nonequilibrium,inductive discharge,effects of Lorentz force were made clear through the present study.It was clarified that the thermal nonequilibrium model played an important role in properly predicting the temperature field.The prediction accuracy can be improved by applying the 3rd AETP to the simulation for this ICPWT.

Exact Solution of Klein-Gordon Equation by Asymptotic Iteration Method

Using the asymptotic iteration method （AIM） we obtain the spectrum of the Klein-Gordon equation for some choices of scalar and vector potentials. In particular, it is shown that the AIM exactly reproduces the spectrum of some solvable potentials.

The Nonzero External Magnetic Field of Long Solenoids

A widespread assertion has existed for a long time, believing the external field of an infinitely long solenoid should be zero, but it is proofed to be wrong in this work. The components of magnetic flux density of current-carrying, closely wound cylindrical solenoids are calculated. At a distant field point, the external field definitely has a nonzero component, being equal to that of a straight wire of equal length. Since this equivalence is length-independent, it still holds true for ideal solenoids having infinite length. Hence the incorrect and still spreading inference about long solenoids should be rectified. Furthermore, theoretical and experimental discussions involving solenoids should be reviewed again carefully.

BASIC SOLUTION FOR THE THREE-PHASE COMPOSITE CONSTITUTIVE MODEL IN ANTIPLANE PIEZOELECTRICITY

A basic solution in series form for the three-phase composite cylindrical model in antiplane piezoelectricity subjected to the action of a singularity in the intermediate matrix region is presented. The solution is obtained through the complex potential approach in conjunction with the techniques of analytical continuation, singularity analysis, Laurent series expansion in an annular region and Cauchy integral formulae, etc. Based on the complex potentials obtained, explicit expressions for the distribution of stress and electric displacement in the three regions are also derived.

The Quasi-Exactly Solvable Problems in Relativistic Quantum Mechanics

We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein–Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.

Numerical Implementation of Meshless Method for Electromagnetic Field Governing Equations

For electromagnetic governing equations formulated by magnetic vector potential and electric scalar potential,its detailed numerical implementation is achieved by using meshless method and Galerkin approach.And essential boundary and interface condition of electromagnetic field are imposed by means of Lagrange multiplier method.Furthermore,the influences of interpolation point number at essential boundary and interface on computational results are also discussed.Examples are given to validate the effects of meshless method and Lagrange multiplier approach for electromagnetic field.

Further Support of the Reliability of the Limit on Photon Mass Given by the Rotating Torsion Balance Experiment

We consider there is a vacancy in the plasma in the solar system,and calculate the vector potential produced by the magnetic field frozen in the plasma.The result shows that,in the vacancy,the vector potential produced by the magnetic field frozen in the plasma is much less than the large scale cosmic vector potential.This means if our earth is in such a vacancy,the total vector potential on the surface of the earth is dominated by the cosmic magnetic vector potential,which gives a further support of the reliability of the limit on photon mass given by rotating torsion balance experiment [Phys.Rev.Lett.90(2003) 081801].

Isotopic Effects on Stereodynamics of the C^+ + H_2→CH^+ + H Reaction

The effects of isotope substitution on stereodynamic properties for the reactions C^+ + H_2/HD/HT →CH^+ + H/D/T have been studied applying a quasi classical trajectory method occurring on the new ground state CH_2^+ potential energy surface [J. Chem. Phys. 142(2015) 124302]. In the center of mass coordinates applying the quasi classical trajectory method to investigate the orientation and the alignment of the product molecule. Differential cross section and three angle distribution functions P(θ_r), P(ф_r), P(θ_r, ф_r) on the potential energy surface that fixed the collision energy with a value is 40 kcal/mol have been studied. The isotope effect becomes more and more important with the reagent molecules H_2 changing into HD and HT. P(θ_r, ф_r) as the joint probability density function of both polar angles θ_r and ф_r, which can illustrate more detailed dynamics information. The isotope effect is obvious influence on the properties of stereodynamics in the reactions of C^+ + H_2/HD/HT → CH^+ + H/D/T.