Representation ground

In eq. (4) the cosets themselves are used as a basis for G, and from eq. (3) gs H is transformed into gr H by gj. Since the operator gy simply re-orders the basis, each matrix representation in the ground representation Tg is a permutation matrix (Appendix A1.2). Thus the 5th column of T8 has only one non-zero element,... 

Table 4.10. The ground representation Te determined from the cosets P0 H, P3 H by using the cosets as a basis, eq. (4.8.4).

Exercise 4.8-1 The dimension of the ground representation is equal to the number of cosets, t = g/h. 

This permutational representation is also called the ground representation. It describes the transformation of the coset space. The dimension of this coset space is G / //. In the case of a cluster, where each coset corresponds to a site, it represents the permutation of the positions of the sites. For this reason, it is also called the positional representation. Indeed, Eq. (4.72) may equally well be written as... 

There are three ways to represent power and ground when writing out EDIF from Synopsys. They can be represented as ports, cells, or nets. It is determined by the edifout power and ground representation variable. 

Net representation Some ASIC vendors support nets as power and ground representation. The cdifout j>ower and ground representation variable must be set to a value net. Also, the following variables are used to identify the power and ground nets. 

Note that h is simply the diagonal matrix of zeroth-order eigenvalues In the following, it will be assumed that the zeroth-order eigenfunction a reasonably good approximation to the exact ground-state wavefiinction (meaning that Xfi , and h and v will be written in the compact representations... 

The off-diagonal elements in this representation of h and v are the zero vector of lengtii (for h) and matrix elements which couple the zeroth-order ground-state eigenfunction members of the set q (for v) ... 

Figure Al.6.24. Schematic representation of a photon echo in an isolated, multilevel molecule, (a) The initial pulse prepares a superposition of ground- and excited-state amplitude, (b) The subsequent motion on the ground and excited electronic states. The ground-state amplitude is shown as stationary (which in general it will not be for strong pulses), while the excited-state amplitude is non-stationary. (c) The second pulse exchanges ground- and excited-state amplitude, (d) Subsequent evolution of the wavepackets on the ground and excited electronic states. Wlien they overlap, an echo occurs (after [40]).

Figure C 1.2.9. Schematic representation of photo induced electron transfer events in fullerene based donor-acceptor arrays (i) from a TTF donor moiety to a singlet excited fullerene and (ii) from a mthenium excited MLCT state to the ground state fullerene.

Single surface calculations with a vector potential in the adiabatic representation and two surface calculations in the diabatic representation with or without shifting the conical intersection from the origin are performed using Cartesian coordinates. As in the asymptotic region the two coordinates of the model represent a translational and a vibrational mode, respectively, the initial wave function for the ground state can be represented as. 

The electronic configuration for an element s ground state (Table 4.1) is a shorthand representation giving the number of electrons (superscript) found in each of the allowed sublevels (s, p, d, f) above a noble gas core (indicated by brackets). In addition, values for the thermal conductivity, the electrical resistance, and the coefficient of linear thermal expansion are included. 

Figure 20.1 Phasor representation of an unbalanced power system on a ground fault...

With an increase in the length of the buried ground conductors, the value of their ground resistance diminishes. It has been found that equation (22.13) is more accurate for a grid depth up to 250 mm. At greater depths of station grids, a moi e accurate representation is found in the following equation ... 

Fig. 13.5. Schematic representation of the potential energy surfaces of the ground state (S ,) and the excited state (.5,) of a nonadiabatic photoreaction of reactant R. Depending on the way the classical trajectories enter the conical intersection region, different ground-state valleys, which lead to products P and can be reached. Reproduced from Angew. Chem. Int. Ed. Engl. 34 549 (1995) by permission of Wiley-VCH.

Fig. 5 Schematic representation of the electronic transitions during luminescence phenomena [5]. — A absorbed energy, F fluorescence emission, P phosphorescence, S ground state. S excited singlet state, T forbidden triplet transition.

Figure 16-14. One-dimensional representation of the ground- and cxcitcd-slalc potential surfaces for irons- and m-stilbene [721.

As described above, the ground state vibrational wavefunction is totally symmetric for most common molecules. Therefore, the product, -(1)0 must at least contain a totally symmetric component. The direct product of two irreducible representations contains the totally symmetric representation only if the two irreducible representations are identical. Therefore, transitions can occur from a symmetrical initial state only to those states that have the same symmetry properties as the transition operator, 0. 

If the hamiltonian is truly stationary, then the wx are the space-parts of the state function but if H is a function of t, the wx are not strictly state functions at all. Still, Eq. (7-65) defines a complete orthonormal set, each wx being time-dependent, and the quasi-eigenvalues Et will also be functions of t. It is clear on physical grounds, however, that to, will be an approximation to the true states if H varies sufficiently slowly. Hence the name, adiabatic representation. 

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