Showing papers on "Electromagnetic field published in 1969"
TL;DR: The theory of explicitly time-dependent invariants for quantum systems whose Hamiltonians are explicitly time dependent was developed in this article, where the authors derived a simple relation between eigenstates of such an invariant and solutions of the Schrodinger equation.
Abstract: The theory of explicitly time‐dependent invariants is developed for quantum systems whose Hamiltonians are explicitly time dependent. The central feature of the discussion is the derivation of a simple relation between eigenstates of such an invariant and solutions of the Schrodinger equation. As a specific well‐posed application of the general theory, the case of a general Hamiltonian which settles into constant operators in the sufficiently remote past and future is treated and, in particular, the transition amplitude connecting any initial state in the remote past to any final state in the remote future is calculated in terms of eigenstates of the invariant. Two special physical systems are treated in detail: an arbitrarily time‐dependent harmonic oscillator and a charged particle moving in the classical, axially symmetric electromagnetic field consisting of an arbitrarily time‐dependent, uniform magnetic field, the associated induced electric field, and the electric field due to an arbitrarily time‐dependent uniform charge distribution. A class of explicitly time‐dependent invariants is derived for both of these systems, and the eigenvalues and eigenstates of the invariants are calculated explicitly by operator methods. The explicit connection between these eigenstates and solutions of the Schrodinger equation is also calculated. The results for the oscillator are used to obtain explicit formulas for the transition amplitude. The usual sudden and adiabatic approximations are deduced as limiting cases of the exact formulas.
1,613 citations
TL;DR: In this article, the power spectrum of the light scattered by a two-level atom driven near resonance by a monochromatic classical electric field is evaluated, where the atom is assumed to relax to equilibrium with the driving field via radiation damping, which is treated by explicitly coupling the atom to quantized electromagnetic field modes.
Abstract: The power spectrum of the light scattered by a two-level atom driven near resonance by a monochromatic classical electric field is evaluated. The atom is assumed to relax to equilibrium with the driving field via radiation damping, which is treated by explicitly coupling the atom to the quantized electromagnetic field modes. The power spectrum of the scattered field is directly obtainable from the two-time atomic dipole moment correlation function, which is evaluated by a method based on a Markoff-type assumption analogous to that used to evaluate the time evolution of single-time atomic expectation values.
1,357 citations
TL;DR: In this article, a computer analysis of the propagating modes of a rectangular dielectric waveguide is presented, based on an expansion of the electromagnetic field in terms of a series of circular harmonics multiplied by trigonometric functions.
Abstract: This paper describes a computer analysis of the propagating modes of a rectangular dielectric waveguide. The analysis is based on an expansion of the electromagnetic field in terms of a series of circular harmonics, that is, Bessel and modified Bessel functions multiplied by trigonometric functions. The electric and magnetic fields inside the waveguide core are matched to those outside the core at appropriate points on the boundary to yield equations which are then solved on a computer for the propagation constants and field configurations of the various modes. The paper presents the results of the computations in the form of curves of the propagation constants and as computer generated mode patterns. The propagation curves are presented in a form which makes them refractive-index independent as long as the difference of the index of the core and the surrounding medium is small, the case which applies to integrated optics. In addition to those for small index difference, it also gives results for larger index differences such as might be encountered for microwave applications.
549 citations
TL;DR: In this paper, the Rarita-Schwinger equation in an external electromagnetic potential is shown to be equivalent to a hyperbolic system of partial differential equations supplemented by initial conditions.
Abstract: The Rarita-Schwinger equation in an external electromagnetic potential is shown to be equivalent to a hyperbolic system of partial differential equations supplemented by initial conditions. The wave fronts of the classical solutions are calculated and are found to propagate faster than light. Nevertheless, for sufficiently weak external potentials, a consistent quantum mechanics and quantum field theory may be established. These, however, violate the postulates of special relativity.
394 citations
TL;DR: In this article, the structure of the electromagnetic stress-energy tensor in the region between the plates for finite temperatures as well as for the zero-temperature limit was discussed, and the relationship of its components to the thermodynamic variables of the radiation field was described.
Abstract: The zero-point fluctuations of the electromagnetic field give rise to an attractive force between two perfectly conducting parallel plates, the Casimir force. We discuss the structure of the electromagnetic stress-energy tensor in the region between the plates for finite temperatures as well as for the zero-temperature limit, and we describe the relationship of its components to the thermodynamic variables of the radiation field. The stress-energy tensor is defined so that infinite quantities never appear, and it is explicitly computed with the aid of an image-source construction of the Green's function. The finite-temperature case involves both an infinite set of spatial images and an infinite sum of temperature-dependent images.
379 citations
TL;DR: Light pulses propagation in nonlinear laser medium, obtaining equations of motion for density matrix was studied in this paper, where it was shown that light pulses propagate in a nonlinear nonlinear medium.
Abstract: Light pulses propagation in nonlinear laser medium, obtaining equations of motion for density matrix
241 citations
TL;DR: In this paper, the Drell-Hearn-Gerasimov sum rule and the low energy theorem for Compton scattering for composite systems were derived from Lagrangian field theory, with specific reference to the fine structure and Lamb shift measurements.
164 citations
TL;DR: In this paper, the transient fields from a finite horizontal loop excited by a half sine wave current pulse have been computed numerically for a particular source receiver configuration at a height of 100 meters above a layered ground.
Abstract: The transient fields from a finite horizontal loop excited by a half sine wave current pulse have been computed numerically for a particular source receiver configuration at a height of 100 meters above a layered ground. The amplitude of the vertical component of the magnetic field has been chosen for the interpretation. Curves of apparent conductivity vs. time, plotted during the off-time of the signal, show that layering is easily resolved, that resonance effects are present and that polarization effects are detectable for certain types of polarization.
124 citations
TL;DR: An exact solution of the discontinuity problem of a circular cylindrical post of arbitrary complex permittivity centered in a rectangular waveguide with the axis parallel to the electric field vector of the dominant mode has been set up and numerical results based directly on this solution have been found as discussed by the authors.
Abstract: An exact solution of the discontinuity problem of a circular cylindrical post of arbitrary complex permittivity centered in a rectangular waveguide with the axis parallel to the electric field vector of the dominant mode has been set up and numerical results based directly on this solution have been found rising an electronic computer. The method used divides the waveguide up into three different regions by introducing two imaginary plane walls perpendicular to the waveguide walls. In the center region, which contains the cylindrical rod, the electromagnetic field is expanded in cylindrical waves and in the outer regions the field is expanded in waveguide modes. By setting up the boundary conditions at all discontinuity surfaces and performing numerical matching of the fields at the two imaginary walls, a system of linear equatious determining the coefficients of reflection, transmission, and absorption of the field due to the cylindrical rod is found. The structure which is of most interest in the case of a plasma column is a coaxial structure consisting of an inner dielectric cylinder with complex permittivity (the plasma) surrounded by a dielectric sleeve with real, positive permittivity (the glass tube). The theory is therefore developed to apply generally for such structures. From the numerical results, curves have been obtained showing the relationship between the coefficients of reflection and transmission and the (complex) permittivity of the rod material. Such curves maybe used for deducing the microwave properties of a cylindrical rod from measurements of the reflection and transmission coefficient of the rod.
88 citations
TL;DR: In this article, a general covariant set of electromagnetic field equations and associated constitutive relations is developed to deal with electromagnetic radiation in arbitrarily moving media, which is sufficiently general to include dispersive as well as nonisotropic media.
Abstract: A generally covariant set of electromagnetic field equations and associated constitutive relations is developed to deal with electromagnetic radiation in arbitrarily moving media. The equations are sufficiently general to include dispersive as well as nonisotropic media. Several special cases are investigated to illustrate the method and to demonstrate the consistency of the formulation.
TL;DR: In this article, coherent states and the Green function are constructed for a charged particle in a time-dependent magnetic field, and a new invariant, coherent states, is constructed.
TL;DR: In this article, the frequency conversion of electromagnetic fields is treated quantum mechanically through an analysis of a simple theoretical model, where two modes of the field are coupled by a parameter which oscillates at the difference frequency.
Journal Article•
TL;DR: In this article, the authors show the basic similarity of acoustic and electromagnetic field equations and exploit this fact in applying microwave methods to acoustic resonator and waveguide problems, using symbolic notation, rather than tensor subscripts, for the acoustic fields.
Abstract: During the past 20 years the value of the microwave approach to electromagnetic field problems has been amply demonstrated. The purpose of this paper is to show the basic similarity of acoustic and electromagnetic field equations and to exploit this fact in applying microwave methods to acoustic resonator and waveguide problems. This is accomplished most directly and efficiently by using symbolic notation, rather than tensor subscripts, for the acoustic fields. The usefulness of this notation is illustrated by the problems of plane wave propagation and piezoelectric stiffening in an anisotropic medium, and by derivations of Poynting's and reciprocity theorems for a piezoelectric medium. Piezoelectric resonators are treated in detail from the point of view of normal mode expansions. A general network representation is obtained and is applied to the disk transducer, as an example. Normal mode theory of piezoelectric waveguides is briefly sketched and a perturbation theorem, which can be applied to both resonator and waveguide problems, is derived.
TL;DR: In this paper, the classical Sommerfeld problem of electromagnetic wave propagation over a flat earth is reformulated by using the electromagnetic compensation theorem, and the solution is carried through without recourse to the usual spectral representation of the potential function, and therefore complicated contour integrations are avoided in the subsequent evaluation.
Abstract: The classical Sommerfeld problem of electromagnetic wave propagation over a flat earth is reformulated by using the electromagnetic compensation theorem. The solution is carried through without recourse to the usual spectral representation of the potential function, and therefore complicated contour integrations are avoided in the subsequent evaluation. Using reciprocity and duality, the complete electromagnetic fields are calculated for elemental vertical or horizontal dipoles of both electric and magnetic types, which are elevated above an arbitrary but passive surface impedance such as that corresponding to homogeneous, horizontally stratified, or uniformly rough surfaces. The results are identical to the little known but more accurate work of Norton, and under certain approximations they reduce to the more well-known results of Norton, Hufford, Bremmer, and others. The restrictions on the impedance properties of the surface are given, and certain direction finding errors are discussed. It is shown that the index of refraction contrast between the upper and lower medium need not be large.
TL;DR: In this article, an explicit expression for GLAUBER's P-function representing the state of the electromagnetic field after amplification is found, interpreted as a classical distribution function for the complex amplitude of the field, a distribution function W(φ; t) for the phase is obtained by averaging over the real amplitude.
Abstract: Extending recent calculations of GLASSGOLD and HOLLIDAY [3] the amplification process by means of a laser amplifier is treated theoretically in case of an arbitrary quantum mechanical state of the incident electromagnetic field. An explicit expression for GLAUBER's P-function representing the state of the field after amplification, is found. Interpreting this function as a classical distribution function for the complex amplitude of the field, a distribution function W(φ; t) for the phase is obtained by averaging over the real amplitude. With the help of W(φ; t) the phase uncertainty (δφ)2 for the amplified field is calculated. The result approximately agrees with the expression for(δφ)2 following from the phase operator originally introduced by HEITLER if applying it to the incident field. Thus a connection between the phase operator and an experimental arrangement is established.
TL;DR: Theoretical and experimental aspects of the diffraction of gaussian laser beams by the straight edge bounding an opaque plane are investigated in this article, based upon the Kirchhoff scalar wave theory in the Fresnel limit.
Abstract: Theoretical and experimental aspects of the diffraction of gaussian laser beams by the straight edge bounding an opaque plane are investigated. Theoretical analysis is based upon the Kirchhoff scalar wave theory in the Fresnel limit, assuming an incident electromagnetic field having spatial amplitude and phase variation appropriate to a fundamental-mode gaussian beam. Experimental observation consisting of irradiance as a function of position is in good agreement with this theory. Both theoretical and experimental results are found to depend strongly on gaussian-beam parameters.
TL;DR: In this paper, the authors extended quantum field calculations to include atomic field effect on atom, predicting spontaneous decay rate from excited state and light frequency time dependence, and extended the quantum field calculation with atomic field effects on atom.
Abstract: Unquantized field calculations extended to include atomic field effect on atom, predicting spontaneous decay rate from excited state and light frequency time dependence
TL;DR: In this paper, the problem of the electromagnetic shielding effectiveness of an electrically thin, nonmagnetic, plane metal sheet of infinite extent on the electromagnetic field generated by a circular loop field source with uniform current I is solved by application of the quasi-near field approximations to the exact integral expressions.
Abstract: The problem of the electromagnetic shielding effectiveness of an electrically thin, nonmagnetic, plane metal sheet of infinite extent on the electromagnetic field generated by a circular loop field source with uniform current I is solved by application of the quasi-near field approximations to the exact integral expressions. The results are shown to be in excellent agreement with experimental data as well as numerical integration results.
TL;DR: In this paper, the authors have been recording at Ahmedabad the field strengths of radio waves of 164 kHz transmitted from Tashkent, and a pronounced minimum recurred night after night in the months April to July, the local time of the minimum shifting to earlier hours as the days advanced.
Abstract: SINCE early 1960 we have been recording at Ahmedabad the field strengths of radio waves of 164 kHz transmitted from Tashkent. A pronounced minimum recurred night after night in the months April to July, the local time of the minimum shifting to earlier hours as the days advanced from April to July.
TL;DR: In this paper, it was shown that the momentum of a transverse electromagnetic (TEM) wave packet in a simple, but selfconsistent, model of an electromagnetic material described by time and field-independent scalars e and μ, is given by ∫ D × B d V or ∫ ( E × H )/c 2 d V.
TL;DR: In this article, the authors discuss the electromagnetic ϱ-ω mixing in the light of recent experimental data in the ω → 2π transition and discuss the effect of the φ → φ transition on the mixing of the electromagnetic signal.
TL;DR: In this paper, the electrodynamics of a spin-one particleantiparticle using a (1, 0) 0 (0, 1) six-component wave function are developed.
Abstract: In this paper the electrodynamics of a spin-one particleantiparticle is developed using a (1, 0) 0 (0, 1) six-component wave function. Anomalous magnetic dipole and electric quadrupole effects are included. The wave equation is manifestly covariant and has no auxiliary conditions. The invariant integral for the system is derived and the nonrelativistic limit is discussed.
TL;DR: In this paper, a detailed diseussion of the interpretation of a seattering process within the framework of relativistic quantum mechanics is presented, particularly suited to the seattering of charged scalar particles in an external electromagnetic field.
Abstract: We present a detailed diseussion of the interpretation of a seattering process within the framework of relativistic quantum mechanics. This argument is particularly well suited to the seattering of charged scalar particles in an external electromagnetic field, but it breaks down for spin-1/2 particles. In the latter case, we can improve certain features if we use the Klein-Gordon equation instead of the Dirae equation.
TL;DR: In this paper, a general transport theory of the electronic contribution to the acoustic attenuation and amplification in nondegenerate semiconductors is presented and the results are compared with the approximations for low (ql 1) frequencies.
Abstract: A general transport theory of the electronic contribution to the acoustic attenuation and amplification in nondegenerate semiconductors is presented. External electric and magnetic fields are applied parallel to the acoustic wavevector. The piezoelectric and the deformation potential coupling mechanisms have been taken into account together with self‐consistent electromagnetic fields. The classical theory predicts that there is no dependence of the attenuation on longitudinal magnetic field. A numerical example has been fully developed and the results are compared with the approximations for low (ql 1) frequencies. The values of both the frequency and amplification coefficient for the frequency of maximum amplification are found to be larger in the exact theory than those found by extrapolation of the ql<1 approximation.
Journal Article•
TL;DR: In this paper, it was found that the amplitudes of the component harmonic oscillations of the tortuous paths diminish approximately as the inverse 3/2 power of the oscillation frequency.
Abstract: A possible source of low-frequency electromagnetic radiation from lightning is the tortuous path of the return-stroke current. A number of photographs of lightning channels have been measured, and their tortuous paths have been Fourier-analyzed. It has been found that the amplitudes of the component harmonic oscillations of the paths diminish approximately as the inverse 3/2 power of the oscillation frequency. A theoretical analysis of the electromagnetic field strengths radiated from typical tortuous paths indicates maximum values in the low-frequency band of the order of 10–20 μv sec/m, at ranges of approximately 100 km.