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Hamiltonian discussions

We have discussed up to now vibrational spectra of linear and bent triatomic molecules. We address here the problem of rotational spectra and rotation-vibration interactions.3 At the level of Hamiltonians discussed up to this point we only have two contributions to rotational energies, coming from the operators C(0(3]2)) and IC(0(412))I2. The eigenvalues of these operators are... [Pg.108]

The Hamiltonian discussed above for the f-electrons of the 4f" configuration also applies to the 4f 1 core in the 4f 15d configuration. Parameter values for the 4f" 1 core are expected to be similar (though not necessarily identical) to the parameter values for the ground 4f" configuration. They are distinguished from parameters for 4f by appending (If) . [Pg.66]

Results presented here will be derived from the Hamiltonian representation. Although almost all of them may be derived using other methods, I find that the Hamiltonian approach is the simplest in the sense that memory friction is as easy to handle as ohmic friction. The central building block for the parabolic barrier case is the normal mode transformation of the Hamiltonian, discussed in detail in Sec. Ill. A. In Sec. III.B the normal mode transformation is used to construct normal mode free-energy surfaces. [Pg.627]

Resonances are currently observed in collision processes. We will show in this section, how they can be studied in the framework of the partitioning technique by means of the effective Hamiltonians discussed in Section 2. The theory is described below and illustrated by model applications in Section 3.2. [Pg.26]

The Hamiltonian discussed above for the f-electrons of the 4f" configuration also applies... [Pg.66]

Proofs of the existence of universal features have been based on highly simplified model Hamiltonians. Discussion of real disordered materials has been based on highly simplified model band structures possessing these features. Accurate models for real materials are presently beyond our grasp, so we confine ourselves in this paper to simple models. [Pg.102]

For our purposes, there are three important aspects of the density functional method. First, it is in principle exact and provides an alternative to the direct treatment of the full many-body Hamiltonian discussed above. It is therefore relevant to establish rigorous expressions for other physical quantities, such as the stress, in the density functional formalism. Second, for any functional, variational solutions of the equations satisfy all the properties required to derive the requisite theorems for force, stress, and other derivatives. Third, there are local approximations to the exact... [Pg.186]

The High-Field Approximation In most NMR experiments the nuclear Zeeman interaction with the static external magnetic field is much stronger than all other interactions of the nuclear spins. As a result of these differences in the size, it is usually possible to treat these interactions in first order perturbation theory, i.e. use only those terms which commute with the Zeeman Hamiltonian, the so called secular terms. This approximation is called the high field approximation. While the single particle interactions like CSA or quadrupolar interaction have a unique form, for bilinear interactions, one has to distinguish between a homonuclear and a hetero-nuclear case. The secular parts of Hamiltonians discussed in the previous section are collected in Table 1. [Pg.315]

For the nonrelativistic case we may use the spin Hamiltonian discussed in chapter 4,... [Pg.242]

Figure 10.2 Absorption spectrum of adenine dimer (blue dashed line) and monomer (red solid line) obtained at pure electronic level (a) and at vibronic level (b) by adopting the vibronic Hamiltonian discussed in Section 10.3.1.3. It has been computed from the Fourier transform of the autocorrelation function obtained propagating a doorway state. The latter is a delocalized exciton state obtained mixing the two localized exciton states with equal weights. Figure 10.2 Absorption spectrum of adenine dimer (blue dashed line) and monomer (red solid line) obtained at pure electronic level (a) and at vibronic level (b) by adopting the vibronic Hamiltonian discussed in Section 10.3.1.3. It has been computed from the Fourier transform of the autocorrelation function obtained propagating a doorway state. The latter is a delocalized exciton state obtained mixing the two localized exciton states with equal weights.
Before considering the symmetry under permutations of identical particles it is necessary first to say a little ab out the spin of particles. Each particle is specified not only by space variables but also by spin variables. These have not been considered so far because there are no spin operators in the Hamiltonians discussed in the previous sections. Nevertheless spin is, indirectly, very important in the construction of approximate wavefunctions. [Pg.30]


See other pages where Hamiltonian discussions is mentioned: [Pg.245]    [Pg.526]    [Pg.252]    [Pg.319]    [Pg.92]    [Pg.119]    [Pg.154]    [Pg.134]    [Pg.22]    [Pg.433]    [Pg.426]    [Pg.564]    [Pg.263]    [Pg.526]    [Pg.412]    [Pg.69]   
See also in sourсe #XX -- [ Pg.40 , Pg.155 ]




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