Symmetric state

As was shown in the preceding discussion (see also Sections Vin and IX), the rovibronic wave functions for a homonuclear diatomic molecule under the permutation of identical nuclei are symmetric for even J rotational quantum numbers in and E electronic states antisymmeUic for odd J values in and E elecbonic states symmetric for odd J values in E and E electronic states and antisymmeteic for even J values in Ej and E+ electeonic states. Note that the vibrational ground state is symmetric under pemrutation of the two nuclei. The most restrictive result arises therefore when the nuclear spin quantum number of the individual nuclei is 0. In this case, the nuclear spin function is always symmetric with respect to interchange of the identical nuclei, and hence only totally symmeUic rovibronic states are allowed since the total wave function must be symmetric for bosonic systems. For example, the nucleus has zero nuclear spin, and hence the rotational levels with odd values of J do not exist for the ground electronic state f EJ") of Cr. 

This is the steady-state symmetrical fault current, which the faulty circuit may almost achieve in about three or four cycles from commencement of the short-circuit condition at point Oi (Figure 14.5) and which the interrupting device should be able to break successfully. 

The linear combinations of the solutions. Equations (7.15) and (7.16), are also good solutions of the time-dependent Schrodinger equation, Eq. (7.6). For example, there is a state symmetric with respect to the median plane ... 

G. Gerber In our time-resolved experiments on the NaafZ ) state we observe the symmetric stretch even for long delay times. From nanosecond laser and CW laser spectroscopy it is well known that the B state does not decay on femtosecond or picosecond time scales. So I do not see how the decay in the picosecond experiment by Prof. Woste can be understood and how the evolution of the B state symmetric stretch into the pseudorotation and the radial motion can occur. 

Eq. (1) is used to find the d-band width (6.5 eV) once the other parameters of the band shape are determined. Similarly, Eq. (2) is used to determine the s-band width (12.9 eV) of a free-electron density of states symmetric in energy about the middle of the band. The d-band density of states, Nj(E). rises sharply at the lower band edge to about 1.5 states/eV atom then falls off to 0.47 states/eV atom near the middle. With the general shape of Nj. (E) and Ns(E) given, the critical magnitude of Nd( q ), the chemical potential in d-orbital, is determined from the observed linear part of the low-temperature specific heat as follows ... 

The position of the separation point depends on the Reynolds number. At low Reynolds numbers, we have a flow without separation (see Figure 1.7). In a cross flow around a circular cylinder, the separation occurs if the Reynolds number (the cylinder diameter is taken as the characteristic length) is greater than 5 [486]. For 5 < Re < 40, a separation region with steady-state symmetric adjacent vortices is formed (there is no boundary layer yet). 

Figure 13.26 summarizes schematically the different energetic situations for symmetric gap-states. Symmetric gap-states are proposed by several calculations from Bredas [187,188] and Heeger [185], whereas Springborg [189] finds asymmetrically lying states. Bertho and Jouanin [190] find nearly symmetric polaron and asymmetric bipolaron states. 

As was shown in the preceding discussion (see also Sections VIII and IX), the rovibronic wave functions for a homonuclear diatomic molecule under the permutation of identical nuclei are symmetric for even J rotational quantum numbers in and electronic states antisymmetric for odd J values in and electronic states symmetric for odd J values in S7 and electronic... 

The asymmetric reconstruction, the buckling of the ionic state Contrary to the covalent state, the ionic component should be stabilized by an asymmetric distortion if this one accommodates a positive charge on one side and a negative charge on the other one. The asymmetry allows to mix the first excited state (antisymmetric and ionic) with the upper component of the doubly excited state (symmetric and ionic) and thus to localize the electrons on a single-atom dimer. 

Assuming, as before, that the singlet state (symmetric spatial wavefunction, antisymmetric spin wavefunction) is the ground state, the spatial probability density at large R is given by... 

The rules for labeling these irreducible representations are summarized in Table 6.5. The labels 2, II, A, and so on are used only for the linear molecule groups Ccov and D h- For the nonlinear molecules, A and B states are nondegenerate (with A states symmetric with respect to rotation about the principal axis), E states are doubly degenerate, T or F states are triply degenerate, and G states are fourfold degenerate. Subscripts and superscripts then provide keys for other symmetry elements (if any), and the u or g subscript always appears if inversion is a member of the group. 

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