Running waves

To get the frequency v in centimeters-, the nonstandard notation favored by spectioscopists, one divides the frequency in hertz by the speed of light in a vacuum, c = 2.998 x lO " cm s-, to obtain a reciprocal wavelength, in this case, 4120 cm-. This relationship arises because the speed of any running wave is its frequency times its wavelength, c = vX in the case of electromagnetic radiation. The Raman spectral line for the fundamental vibration of H2 is 4162 cm-. .., not a bad comparison for a simple model. 

The idea was that all these entities exhibit both wave and particle properties. This double nature taxes our imagination few things differ as much as a beam of particles and a running wave. In a beam of particles, matter is concentrated in small units, whereas a wave spreads continuously over space. Still, wave and particle properties are observed for electrons and other fundamental entities. 

First order Doppler broadening can be eliminated by using a standing wave geometry (i.e. oppositely running waves) to excite the two-photon transition. The fractional second order Doppler shift, v1 c2, is less than 2 x 10-16 at a temperature of 1 mK. 

To obtain the bulk properties of the crystal, the crystal is assumed infinite and the boundary condition for is periodicity within one arbitrary domain containing a large number of unit cells. This boundary condition gives rise to solutions (79) that are running waves modulated by a function Wkm(r) that has the periodicity of [/(r),... 

Although classical mechanics does not provide a diamagnetic contribution to the susceptibility from collective electrons (induced internal currents and surface currents cancel one another out), Landau (383) discovered that the running waves of quantum mechanics are modified by H to give a diamagnetic susceptibility —1/3 that of the paramagnetic susceptibility. Thus... 

With R > RC the Coulomb repulsion of the electrons when they are on the same ion is the dominant electron-interaction term, so that the lowest states correspond to an exact number of electrons on each ion rather than to running waves. Although the mutual repulsion of electrons on the same ion prevents the permanent occupation of... 

We will seek solution in the form of running wave... 

The amplitude of sound pressure PA in a mode without cavitation may be evaluated by the following evident relationship for a plane running wave,... 

One possible solution to the problem of the selective excitation with opposite phases is to use a standing laser field instead of the running wave field. If the laser amplitudes differ by the sign, namely, E = — E/-2 = Eo, and k l iq = —k 2 r2, the Rabi frequencies experienced by the atoms are... 

Fig. 2.6 Saturation of an inhomogeneous line profile (a) Bennet hole and dip produced by a monochromatic running wave with co coq (b) Bennet holes caused by the two counterpropagat-ing waves for co coq and for o) = (joo dashed curve) (c) Lamb dip in the absorption profile o s( )...

In analyzing the self-similar solution of an unsteady rarefaction wave in a gas-vapour mixture with condensation, we will first discuss the situation where the onset of condensation occurs at a saturation ratio of unity. Then, the change in the state of the mixture is continuous. The solution is fully isentropic and follows from the characteristic form of the Euler equations, which for a left running wave is ... 

The shock wave is reflecting on the exit area and becomes a left running wave, putting the fluid at rest behind it at the time of reflection.The grid is also simpler. See Fig. 9. 

For the same type of cp(p) but other values of parameters the structure is generated by a division of the pulse of u behind the front of the running wave. The structure... 

Fig.5.19. Ring resonator with 4 Abbe prisms and a beam splitter. The mirror M reflects waves running counter-clockwise back into the resonator. The gain for the clockwise running wave is therefore higher [5.31b]... 

---