Perturbation electromagnetic field

Stimulated emission That part of the emission which is induced by a resonant perturbing electromagnetic field. The transition between states, n and m, is governed by the Einstein coefficient of stimulated emission, Bnm- CIDNP emission and lasing action are examples of processes which require stimulated emission. 

Not only can electronic wavefiinctions tell us about the average values of all the physical properties for any particular state (i.e. above), but they also allow us to tell us how a specific perturbation (e.g. an electric field in the Stark effect, a magnetic field in the Zeeman effect and light s electromagnetic fields in spectroscopy) can alter the specific state of interest. For example, the perturbation arising from the electric field of a photon interacting with the electrons in a molecule is given within die so-called electric dipole approximation [12] by ... 

The interaction of a molecular species with electromagnetic fields can cause transitions to occur among the available molecular energy levels (electronic, vibrational, rotational, and nuclear spin). Collisions among molecular species likewise can cause transitions to occur. Time-dependent perturbation theory and the methods of molecular dynamics can be employed to treat such transitions. 

Two states /a and /b that are eigenfunctions of a Hamiltonian Hq in the absence of some external perturbation (e.g., electromagnetic field or static electric field or potential due to surrounding ligands) can be "coupled" by the perturbation V only if the symmetries of V and of the two wavefunctions obey a so-called selection rule. In particular, only if the coupling integral (see Appendix D which deals with time independent perturbation theory)... 

The expression for the rate R (sec ) of photon absorption due to coupling V beriveen a molecule s electronic and nuclear charges and an electromagnetic field is given through first order in perturbation theory by the well known Wentzel Fermi golden rule formula (7,8) ... 

A quantum mechanical expression for p can be straight forwardly obtained from perturbation theory (with dipolar perturbation coupling of the molecule with the electromagnetic field). 

The Time Dependent Processes Section uses time-dependent perturbation theory, combined with the classical electric and magnetic fields that arise due to the interaction of photons with the nuclei and electrons of a molecule, to derive expressions for the rates of transitions among atomic or molecular electronic, vibrational, and rotational states induced by photon absorption or emission. Sources of line broadening and time correlation function treatments of absorption lineshapes are briefly introduced. Finally, transitions induced by collisions rather than by electromagnetic fields are briefly treated to provide an introduction to the subject of theoretical chemical dynamics. 

These equations are identical with the high-frequency limit (9.13) of the Lorentz model this indicates that at high frequencies all nonconductors behave like metals. The interband transitions that give rise to structure in optical properties at lower frequencies become mere perturbations on the free-electron type of behavior of the electrons under the action of an electromagnetic field of sufficiently high frequency. 

It is convenient to treat the interaction of atomic electrons with an electromagnetic field in the framework of perturbation theory. 

What has been presented here is a semiclassical theory of TJ 1) quantum electrodynamics. Here the electromagnetic field is treated in a purely classical manner, but where the electromagnetic potential has been normalized to include one photon per some unit volume. Here the absorption and emission of a photon is treated in a purely perturbative manner. Further, the field normalization is done so that each unit volume contains the equivalent of n photons and that the energy is computed accordingly. However, this is not a complete theory, for it is known that the transition probability is proportional to n + 1. So the semiclassical theory is only appropriate when the number of photons is comparatively large. 

What causes the electron density of an optical material to couple and polarize with the electromagnetic field of a light wave To understand this process we need to consider more quantitatively what happens at the molecular level. How does light perturb or couple to the electrons in a molecule ... 

This paper presents an account of the dynamics of electric charges coupled to electromagnetic fields. The main approximation is to use non-relativistic forms for the charge and current density. A quantum theory requires either a Lagrangian or a Hamiltonian formulation of the dynamics in atomic and molecular physics the latter is almost universal so the main thrust of the paper is the development of a general Hamiltonian. It is this Hamiltonian that provides the basis for a recent demonstration that the S-matrix on the energy shell is gauge-invariant to all orders of perturbation theory. 

Interestingly enough, one sees differences between the various variants of Markovian and non-Markovian theories already in static linear absorption spectra. In the regime of second-order perturbation theory in the coupling to the electromagnetic field the linear absorption line-shape / (ui) can be calculated from the Fourier transform of the dipole-dipole correlation function as... 

One can see that the full Hamiltonian consists of three terms, two which describe separately the parts for the atom and the field, and one which represents a coupling between the field (vector potential A) and terms from the atom (operator V,-). Obviously, it is this mixed term which is responsible for the photon-atom interaction. Provided perturbation theory can be applied, this term then acts as a transition operator between undisturbed initial and final states of the atom. Following this approach, one has to verify whether the disturbance caused by the electromagnetic field in the atom is small enough such that perturbation theory is applicable. Hence, one has to compare the terms which contain the vector potential A with an energy ch that is characteristic for the atomic Hamiltonian ... 

The result states that it is justified to neglect the term A2 in equ. (8.5b) and to treat the interaction between an atom and an electromagnetic field by first-order perturbation theory. The interaction operator is then given by... 

Since the molecular system is interacting with a time-dependent perturbation due to a time-dependent electromagnetic field, the Hamiltonian of the total system is given as... 

General Theory of Collision Broadening. A molecular component in an ordinary fluid, in the presence of an electromagnetic field E(w,t) and the collisional perturbation V (u,t), due to interactions with other molecules, will experience a total Hamiltonian ... 

A Perturbation Model for Electromagnetic-Field Interaction with Excitable Cellular Membranes... 

Experimental methodologies for perturbing a chemical reaction at equilibrium are well developed and descriptions of them are widely available.20,21 The choice of method depends on the time scale of the reaction kinetics and the kinds of chemical species whose concentration deviations are to be measured. Techniques as simple as the dilution of one or more chemical species or as complicated as electromagnetic field pulsing can be involved (Fig. 4.1). The basic principles, regardless of methodology, are that an external perturbation (e.g., a change in applied pressure) occurs over a time interval that is very much smaller than the time scales of the reaction kinetics that the mechanism... 

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