Electromagnetic field motion

Both infrared and Raman spectroscopy provide infonnation on the vibrational motion of molecules. The teclmiques employed differ, but the underlying molecular motion is the same. A qualitative description of IR and Raman spectroscopies is first presented. Then a slightly more rigorous development will be described. For both IR and Raman spectroscopy, the fiindamental interaction is between a dipole moment and an electromagnetic field. Ultimately, the two... 

Electronic structure theory describes the motions of the electrons and produces energy surfaces and wavefiinctions. The shapes and geometries of molecules, their electronic, vibrational and rotational energy levels, as well as the interactions of these states with electromagnetic fields lie within the realm of quantum stnicture theory. 

If the applied electromagnetic field is an alternating one, then the electrons and ions are pushed (or pulled) backward and forward as the sign of the field changes. At high frequencies of applied fields, this motion causes multiple collisions between ions and neutral species and between electrons and ions and neutral species. 

Electrons from a spark are accelerated backward and forward rapidly in the oscillating electromagnetic field and collide with neutral atoms. At atmospheric pressure, the high collision frequency of electrons with atoms induces chaotic electron motion. The electrons gain rapidly in kinetic energy until they have sufficient energy to cause ionization of some gas atoms. 

These fluctuations will affect the motion of charged particles. A major part of the Lamb shift in a hydrogen atom can be understood as the contribution to the energy from the interaction of the electron with these zero point oscillations of the electromagnetic field. The qualitative explanation runs as follows the mean square of the electric and magnetic field intensities in the vacuum state is equal to... 

It should be stressed, however, that the introduction of the operator 2(k) in the present context is purely for mathematical convenience. All the subsequent development could also be carried out without its introduction. It is only when we consider the interaction of the quantized electromagnetic field with charged particles that the potentials assume new importance—at least in the usual formulation with its particular way of fixing the phase factors in the operators of the charged fields—since the potentials themselves then appear in the equations of motion of the interacting electromagnetic and matter fields. 

Heisenberg picture, the operators describing the negaton-positon field in the presence of an external (classically prescribed) electromagnetic field, Al(x), satisfy the following equations of motion... 

In the Heisenberg picture the electromagnetic field operators satisfy the equations of motion... 

We shall again postulate commutation rules which have the property that the equations of motion of the matter field and of the electromagnetic field are consequences of the Heisenberg equation of motion ... 

Kinetic energy results from motion, potential energy from position. An electromagnetic field carries energy through space work is motion against an opposing force. 

The Hamiltonian for a charged particle in an electromagnetic field can be obtained from Hamilton s principle and Lagrange s equations of motion (Section 3.3) ... 

The equation of motion for the scalar particle in the electromagnetic field is... 

Close to this limit the displacements of the two types of atom have opposite sign and the two types of atom vibrate out of phase, as illustrated in the lower part of Figure 8.10. Thus close to q = 0, the two atoms in the unit cell vibrate around their centre of mass which remains stationary. Each set of atoms vibrates in phase and the two sets with opposite phases. There is no propagation and no overall displacement of the unit cell, but a periodic deformation. These modes have frequencies corresponding to the optical region in the electromagnetic spectrum and since the atomic motions associated with these modes are similar to those formed as response to an electromagnetic field, they are termed optical modes. The optical branch has frequency maximum at q = 0. As q increases slowly decreases and... 

Retarded orbit-orbit interaction of one electron with the electromagnetic field due to the relative motion of another. 

In the above expressions for C(t), the averaging over initial rotational, vibrational, and electronic states is explicitly shown. There is also an average over the translational motion implicit in all of these expressions. Its role has not (yet) been emphasized because the molecular energy levels, whose spacings yield the characteristic frequencies at which light can be absorbed or emitted, do not depend on translational motion. However, the frequency of the electromagnetic field experienced by moving molecules does depend on the velocities of the molecules, so this issue must now be addressed. 

First of all, the theory presented is based on a few assumptions, which, while valid for the molecular systems considered in the literature so far, need to be care-fidly examined in every specific case. As mentioned in Section 8.3, we assume that the effects of external fields on the kinetic energy operator for the relative motion are negligible and that the interactions with electromagnetic fields are independent of the relative separation of the colliding particles. In addition, we ignore the nonadiabatic interactions that may be induced by external fields and that, at present, cannot be rigorously accounted for in the coupled channel calculations. 

The nature of the dual vector ( ) can be deduced without using any equation of motion, but the dual 4-vector is a fundamental geometric property in the four dimensions of spacetime. The complete description of the electromagnetic field in 0(3) electrodynamics must therefore involve boosts, rotations, and spacetime translations, meaning that is a fundamental geometric property of spacetime. The unit 4-vector i M is orthogonal to the unit 4-vector... 

B. A. Hess The reason that macroscopic motions display coherence is that they are in most cases at the classical limit of quantum dynamics. In this case, a suitable occupation of quantum states ensures that quantum mechanical expectation values equal the classical value of an observable. In particular, the classical state of an electromagnetic field (the coherent state) is one in which the expectation value of the operator of the electromagnetic field equals the classical field strengths. 

Furthermore, it was shown in Section II.C that the semisum of the two helicities = (/im + he) = na, which we call the electromagnetic helicity, is a constant of the motion for any standard electromagnetic field in empty space ... 

Definitions for electromagnetic field in Eqs. (79) and (80) are similar to Hofer s [99]. There is a difference we start from an equation of motion for a 4D ether, while Hofer starts from a wave equation for 3D momentum density (his eq. 16). Our B is also similar to Marmanis [100], but his E is quite different. 

In summary, the photon has been modeled as a doublet in rotation in the preferred frame E. Spin and energy have been obtained from a semiclassical analysis. Polarization corresponds to a fixed direction of vector L in E. In a nonpolarized photon vector L has a time-dependent direction. A particular case of nonpolarization is the ellipsoid, as in Hunter and Wadlinger [37]. Our Eq. (96) allows for the existence of multiphotons that vary in steps of half the ground-state photon energy such prediction differs of the prediction of Hunter and Wadlinger [37]. Photons in motion with respect to E will be considered elsewhere. The photon is the source of the electromagnetic field, as explained next. 

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