Spatial quantization

Raum-mass, n. measure of capacity or volume, cubic measure, -menge,/. amoimt of space, volume, -meter, m. cubic meter, -modell, n. space model, -orientierung,/. orientation in space, -quantelung, /. spatial quantization. -richtung,/. direction in space, -strahl,... 

The calculated energy of interaction of an atomic moment and the Weiss field (0.26 uncoupled conduction electrons per atom) for magnetic saturation is 0.135 ev, or 3070 cal. mole-1. According to the Weiss theory the Curie temperature is equal to this energy of interaction divided by 3k, where k is Boltzmann s constant. The effect of spatial quantization of the atomic moment, with spin quantum number S, is to introduce the factor (S + 1)/S that is, the Curie temperature is equal to nt S + l)/3Sk. For iron, with 5 = 1, the predicted value for the Curie constant is 1350°K, in rough agreement with the experimental value, 1043°K. 

The z component of Z may have any value up to +lh. The possible values of lz can be represented as the projection of a vector of length Z on the z axis (Fig. E.9). This situation is referred to as spatial quantization. Only certain values of Z2 are allowed. Due to the uncertainty principle, the values of /, and ly are completely uncertain. In the language of Figure E.9, the vector representing Z is rotating about the z axis, so that Z and lz are fixed, but 1, and Zv are continuously changing. 

Fig. 3.7. Spatial quantization of the angular momentum Ja with quantum number J" = 3 at Q-absorbtion (x = 2) of linearly polarized light with E z. The figures show the values of M" = p. The solid line indicates the spatial distribution of Ja in the classic limit (J —> oo).

F G. 7—4a, 6, c.—Spatial quantization of Bohr-Sommerfeld orbits withfc — 1, 2. 

Highly monodisperse ZnSe nanocrystallites (NCs) were deposited on free-standing porous silieon. Optical phonons confined in nearly spherical ZnSe QDs have been studied theoretically and experimentally. Spatially quantized phonon modes are considered in the framework of the continuum model. Raman scattering and absorption of far-infrared (FIR) radiation in ZnSe quantum dots have been studied. Experimental FTIR transmittance spectra of porous silicon free layers containing nearly spherical ZnSe nanocrystals show a broad band between the bulk TO and LO phonon frequencies. 

In our problem the probability aspects are related to the preceding spatial quantization (refer again to Fig. 4 and 5, and to Fig. 6). The probability to find a specific rock composition Co on the field is proportional to the ratio of the surface covered by Co to the total sur ce of outcrop of transformed rocks (Fig. 6). The spatial spreading of a composition (Le. the proportion of the composition with respect to the whole of the transformed rocks) is proportional to the difference of the velocities of the compositions before and after it. This statement allows to compute the probability density p of co in the scalar case p is proportional to f "(cq). In the case of systems, p is proportional to VXk-Hc (scalar product with eigen vector it is the co-ordinate of VXk along rk). 

As a smnmary, in our problem, there is a spatial quantization whenever there is a differential movement and a non-linear interaetion between a moving entity (here fluid) and matter this is not a property of solid (nor fluid) matter by itself it is a collective or cooperative effect. The thermodynamic properties of the solid solution are n st important to predict the overall structure. The quantization condition is derived from the second... 

Because of the fact that not the absolute value of the angular momentums but their projections are measurable quantities, it can often be said that the electron spin is (1/2)S or simply (1/2). The spin spatial quantization is depicted in Figure 7.21. 

In conclusion, we have established that the precession gives a gain of additional energy. Therefore, to treat spatial quantization of the angular momentum (7.5.3) as precession is incorrect from our point of view, because this effect does not produce any specific energy. 

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