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Spectral projector

Equation (17) is based on the fact that the spectral density operator h E - ft) projects any 2 function (or wave packet) into the space of solutions of the Schrodinger equation at the energy E. However, since the functions are needed only inside interaction region and do not have to be properly normalized, the 8( - ft) in Eqs. (17) and, consequently, (18) can be replaced by any other projector onto the solution space inside the interaction region. A convenient form for such a spectral projector related to Eq. (9) is... [Pg.282]

Thus, use of the spectral projector W implies the following symmetric expression for the A1 matrices ... [Pg.283]

Figure 1.2 Spectral transmittances of the filters. The filters were placed in front of the projectors which were used to illuminate the Mondrian image. (Reproduced from Land EH and McCann JJ 1971 Lightness and retinex theory. Journal of the Optical Society of America 61(1), 1-11, by permission from The Optical Society of America.)... Figure 1.2 Spectral transmittances of the filters. The filters were placed in front of the projectors which were used to illuminate the Mondrian image. (Reproduced from Land EH and McCann JJ 1971 Lightness and retinex theory. Journal of the Optical Society of America 61(1), 1-11, by permission from The Optical Society of America.)...
Wc have omitted the six freciuencies corresponding to rotational and translational motions of the whole cluster. One of the advantages of the INM analysis is that we can perform projections of the density of states. One can decompose the density of states spectrum, c.g., into molecular rotational and translational motion [39]. For molecular clusters it is interesting to explore the localization of the motion described by the Hessian eigenvectors at different frequencies. Even though the harmonic motion is inherently collective, certain motions can be attributed to a limited area. This is the case of non-homogeneous systems, where the spectral characteristics can be quite different for different spatial parts. We define a projector Parea... [Pg.478]

Because is an extensive properly (i.e., size consistent), we should expect possible size inconsistency from the last term in Ej if the (second-order) factor in front of Ej is also extensive would then contain terms that are proportional to the square of the system s size (for identical noninler-acting subsystems). Let us now look at this situation more closely. By introducing the spectral representation of the projector Q given in Eq. (3.21), Ej- can be written as... [Pg.73]

As we have pointed out at several instances the present equations are essentially analogous to the development of suitable master equations in statistical mechanics [4-7], where the wavefunction here plays the role of suitable probability distributions. Note for instance the similarity between the reduced resolvent, based on J-[ (z), and the collision operator of the Prigogine subdynamics. The eigenvalues of the latter define the spectral contributions corresponding to the projector that defines the map of an arbitrary initial distribution onto a kinetic space obeying semigroup evolution laws, for more details we refer to Ref. [6] and the following section. [Pg.7]


See other pages where Spectral projector is mentioned: [Pg.283]    [Pg.283]    [Pg.242]    [Pg.478]    [Pg.97]    [Pg.461]    [Pg.57]    [Pg.129]    [Pg.2498]    [Pg.344]    [Pg.107]    [Pg.146]    [Pg.129]    [Pg.1527]    [Pg.363]    [Pg.377]    [Pg.144]    [Pg.16]    [Pg.230]   
See also in sourсe #XX -- [ Pg.283 ]




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