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Potential function, Fourier component

Wave functions in position and momentum spacce are related as in (III. 16), and the Fourier component of the potential is... [Pg.137]

In density functional theories the potential is determined by the density, and consequently its Fourier components are related to those of the density. One can therefore connect the symmetry properties of the momentum funetions, in other words the transformation... [Pg.137]

Here /i g(u) is the Fourier components of the image intensity function. u is the lattice vector in reciprocal space. F (u) is the Fourier spectmm of the projected potential y>,(x, y). In crystallography, F (u) is the structure factor of the crystal. [Pg.261]

As mentioned in section 6, the structure factors F(u) are proportional to the Fourier components lim(u) of the HREM image and the projected potential is proportional to the negative of the image intensity, if the image is taken Scherzer defocus where the contrast transfer function T(u) -1. In general, the Fourier components lim(u) are proportional to the structure factors F(u) multiplied by the contrast transfer function (CTF). The contrast transfer function T(u) = D(u)sinx(u) is not a linear function. It contains two parts an envelope part D(u) which dampens the amplitudes of the high resolution components ... [Pg.287]

The time and frequency domains are related by a simple function, one being the inverse of the other (Fig. 2.17). The complicating factor is that a genuine FID is usually composed of potentially hundreds of components of differing frequencies and amplitude, in addition to noise and other possible artefacts, and in such cases the extraction of frequencies by direct inspection is impossible. By far the most widely used method to produce the frequency domain spectrum is the mathematical procedure of Fourier transformation, which has the general form ... [Pg.24]

Equation (24) shows that the response of the Fourier components of the density of a chain to a change of potential acting on that chain can be expressed in terms of the static structure factor SN(q) of the chain for gaussian chains this is simply the well-known Debye function [2]. [Pg.193]

Soon this concept was connected (234) with the magnitude of the Kj constant in a Fourier component analysis of internal rotation potential functions in molecules exhibiting the anomeric effect (see Section III.B.2). It was also used to account for bond lengths in methanediol (8) (235) and methoxymethanol (49) (244) (p. 196), but the authors claimed (235) that the shortening of the C—O bonds in the ap, ap conformers of 8 cannot be explained by the interaction pictured in Figure 26a. [Pg.252]

How can we understand why Vg > 0 is required to obtain a surface state In order to answer this question, we first have to discuss what Vg> 0 actually means for the potential in the crystal. In the secular Eq. (5.32), only the Fourier components Vg and V g = Vg appear. Hence, the effective potential in the crystal obviously is a simple cosine function ... [Pg.124]

Any function, such as a potential energy function, which has the periodicity defined by (aj, 33,33) can only have Fourier components associated with the following values of q, the variable in the reciprocal space of the Fourier transform ... [Pg.49]

An integrated GC/IR/MS instrument is a powerful tool for rapid identification of thermally generated aroma compounds. Fourier transform infrared spectroscopy (GC/IR) provides a complementary technique to mass spectrometry (MS) for the characterization of volatile flavor components in complex mixtures. Recent improvements in GC/IR instruments have made it possible to construct an integrated GC/IR/HS system in which the sensitivity of the two spectroscopic detectors is roughly equal. The combined system offers direct correlation of IR and MS chromatograms, functional group analysis, substantial time savings, and the potential for an expert systems approach to identification of flavor components. Performance of the technique is illustrated with applications to the analysis of volatile flavor components in charbroiled chicken. [Pg.61]


See other pages where Potential function, Fourier component is mentioned: [Pg.287]    [Pg.2213]    [Pg.81]    [Pg.109]    [Pg.183]    [Pg.44]    [Pg.46]    [Pg.140]    [Pg.126]    [Pg.45]    [Pg.139]    [Pg.216]    [Pg.82]    [Pg.586]    [Pg.2213]    [Pg.159]    [Pg.244]    [Pg.250]    [Pg.526]    [Pg.255]    [Pg.172]    [Pg.46]    [Pg.169]    [Pg.344]    [Pg.1093]    [Pg.330]    [Pg.81]    [Pg.1374]    [Pg.216]    [Pg.26]    [Pg.304]    [Pg.38]    [Pg.692]    [Pg.77]    [Pg.799]    [Pg.155]   


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