Monochromatic waves standing

According to De Broglie an electron in a Bohr orbit is associated with a standing wave. To avoid self destruction by interference an integral number of wavelengts are required to span the orbit of radius r, which implies n — 2nr, or nh/2n = pr, which is the Bohr condition. As a physical argument the wave conjecture is less plausible, but not indefensible. One possible interpretation considers the superposition of several waves rather than a single monochromatic wave to simulate the behaviour of a particle. 

Oscillations with only one frequency are monochromatic waves. Thus each normal mode of oscillation [each term in equation (8)] defines a monochromatic wave. There are special shapes of chambers for which more than one mode may have the same frequency this is called degeneracy and admits an infinite variety of monochromatic wave forms (for example, tangential modes in cylindrical chambers). Most of the normal modes describe standing waves, waves having nodal points for the velocity (points where the velocity is always zero) and for the amplitude of the pressure oscillations. Thus, according to equation (8), longitudinal modes have pressure nodes at nz/l = 1, I,..., and they have velocity nodes at nz/l = 0, 1, 2,..., as... 

The construction of a TXRF system, including X-ray source, energy-dispersive detector and pulse-processing electronics, is similar to that of conventional XRF. The geometrical arrangement must also enable total reflection of a monochromatic primary beam. The totally reflected beam interferes with the incident primary beam. This interference causes the formation of standing waves above the surface of a homogeneous sample, as depicted in Fig. 4.1, or within a multiple-layered sample. Part of the primary beam fades away in an evanescent wave field in the bulk or substrate [4.28],... 

Several approaches can be taken to minimize the effect of standing waves. Since the phenomenon results from coherent interference of monochromatic photons it can be reduced by employing broadband illumination. 

The mathematical expression for the saturable absorption profile of a gaseous probe interacting with a tunable monochromatic standing wave (frequency co, electric vector ) can be deduced as follows... 

One method which employs the saturable absorption of intracavity gaseous absorbers has turned out to be strikingly successful333) As explained in the last section, the absorption profile of a gas interacting with a monochromatic standing wave inside the laser cavity exhibits a sharp minimum at the center of the unsaturated ab-... 

Figure 2. X-ray standing wave field formed in a crystal and above its surface by the interference of incident and Bragg-diffracted monochromatic X-ray plane waves. The inset shows the reciprocal space diagram for the Laue condition described by Equation (4).

The basic types of radiation force can be imderstood using simple models of the quasi-resonant interaction of a two-level atom with the monochromatic field of a laser beam or a standing laser wave, and using simple models describing the interaction of a multilevel atom with a laser field. 

If the absorbing molecules are exposed to a monochromatic standing wave with light frequency co, this field can be composed of two travelling waves propagating in opposite directions. 

Fig.3.19a-c. Saturation by a monochromatic standing wave, (a) Population distribution n(v ) for 03 coq. (b) Absorption coefficient a(o3) of an in-homogeneously broadened line, as obtained when tuning the frequency U3 of the standing wave across the line profile, (c) Saturation of a homogeneous absorption profile... 

In Sect.10.2 it has been discussed in detail that the nonlinear absorption of a molecule in a monochromatic standing wave field leads to the formation of a narrow Lamb dip at the center o)q of a Doppler-broadened absorption line (see Fig.10.19). The Lamb-dip formation may be regarded as a two-step process the depletion of a small subgroup of molecules with velocity components v =... 

When the absorbing probe is placed inside the laser resonator, the standing wave of the monochromatic laser with w + wq burns two holes into the ground state population ng (v ), which appear at the velocity components... 

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