Homogeneous electric field oscillations

Fig. 12.7. Sadlej relation. The electric field mainly causes a shift of the electronic charge distribution toward the anode (a). A GTO represents the eigenfunction of a harmonic oscillator. Suppose that an electron oscillates in a parabolic potential energy well (with the force constant I ). In this situation, a homogeneous electric field corresponds to the perturbation x, that conserres the hannonicity with unchanged force constant k (b).

Indeed, this can be shown as follows. The Schrddinger equation for the harmonic oscillator (here, for an electron with n = 1 in a.u., its position is x) without any electric field is given on p. 186. According to file example of the hydrogen atom in an electric field, the Schrddinger equation for an electron oscillating in homogeneous electric field > 0 takes the form ... 

Let us imagine a molecule immobilized in a laboratory coordinate system (as in an oriented crystal). Let us switch on a homogeneous electric field , which has two components, a static component and an oscillating one with frequency (o ... 

NMR Hamiltonian (p. 768) non-homogeneous electric field (p. 729) nonlinear response (p. 733) nuclear magneton (p. 757) oscillating electric field (p. 752) paramagnetic effect (p. 780) paramagnetic spin-orbit (p. 782)... 

These effects can also be seen as the response functions of the solvent to an external perturbation, and, if the latter is time dependent, such as an external homogeneous electric field which oscillates at frequency w, or a field produced by a subsystem undergoing a chemical reaction, the relaxation times related to each of these functions tk become the quantities which entirely define the solvent behavior. Thus it is to be expected that, as the frequency of the external field increases, nonequilibrium effects will appear successively in the different parts of the polarization. First the motions of molecules and ions (characteristic times above I0 s) will lag behind the variation of the field, next the atoms will not be able to follow the field (characteristic times 10 s) and finally, at very high frequencies, the field will change too fast for the electrons to follow it. 

The return to equilibrium of a polarized region is quite different in the Debye and Lorentz models. Suppose that a material composed of Lorentz oscillators is electrically polarized and the static electric field is suddenly removed. The charges equilibrate by executing damped harmonic motion about their equilibrium positions. This can be seen by setting the right side of (9.3) equal to zero and solving the homogeneous differential equation with the initial conditions x = x0 and x = 0 at t = 0 the result is the damped harmonic oscillator equation ... 

As a consequence of the collective motion of the neutral system across the homogeneous magnetic field, a motional Stark term with a constant electric field arises. This Stark term inherently couples the center of mass and internal degrees of freedom and hence any change of the internal dynamics leaves its fingerprints on the dynamics of the center of mass. In particular the transition from regularity to chaos in the classical dynamics of the internal motion is accompanied in the center of mass motion by a transition from bounded oscillations to an unbounded diffusional motion. Since these observations are based on classical dynamics, it is a priori not clear whether the observed classical diffusion will survive quantization. From both the theoretical as well as experimental point of view a challenging question is therefore whether quantum interference effects will lead to a suppression of the diffusional motion, i.e. to quantum localization, or not. 

In crystalline solids the electric field E(R) at the location R of the excited molecule A has a symmetry depending on that of the host lattice. Because the lattice atoms perform vibrations with amplitudes depending on the tem-peratur T, the electric field will vary in time and the time average E(T, t, R)) will depend on temperature and crystal structure [3.41-3.43]. Since the oscillation period is short compared with the mean lifetime of A ( /), these vibrations cause homogeneous line broadening for the emission or absorption of the atom A. If all atoms are placed at completely equivalent lattice points of an ideal lattice, the total emission or absorption of all atoms on a transition Ei Ek would be homogeneously broadened. 

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