Standing waves, energy

The second model is a quantum mechanical one where free electrons are contained in a box whose sides correspond to the surfaces of the metal. The wave functions for the standing waves inside the box yield permissible states essentially independent of the lattice type. The kinetic energy corresponding to the rejected states leads to the surface energy in fair agreement with experimental estimates [86, 87],... 

Figure Cl.4.5. Population modulation as the atom moves through the standing wave in the Tin-periD-lin one dimensional optical molasses. The population lags the light shift such that kinetic is converted to potential energy then dissipated into the empty modes of the radiation field by spontaneous emission (after 1171).

Fig. 3.17 The two possible sets of standing waves at the Brillouin zone boundary. Standing wave A concentrates electron density at the nuclei, whereas wave B concentrates electron density between the nuclei. Wave A thus has a lower energy than wave B.

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],... 

A three-dimensional (3D) piece of metal can be considered as a crystal of infinite extension in the directions x, y and z with standing waves with the wave numbers k, ky and k, each being occupied with two electrons as a maximum. In a piece of bulk metal the energy differences Sk y are so small that A->0, identical with quasi-free continuously distributed electrons. Since the energy of free electrons varies with the square of the wave numbers, its dependence on k describes a parabola. Figure 4a shows these relations. 

A standing wave (SW) microwave linear accelerator consists of a linear array of resonant cavities that are energized by a common source of microwave power. These cavities are nearly isolated by webs with small-diameter apertures, and the high-energy electron beam passes through these apertures. However, they are coupled through intermediate cavities, which stabilize the microwave phase relationship between the accelerating cavities. 

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