Diagonalization techniques

In general, no simple, consistent set of analytical expressions for the resonance condition of all intradoublet transitions and all possible rhombicities can be derived with the perturbation theory for these systems. Therefore, the rather different approach is taken to numerically compute all effective g-values using quantum mechanics and matrix diagonalization techniques (Chapters 7-9) and to tabulate the results in the form of graphs of geff,s versus the rhombicity r = E/D. This is a useful approach because it turns out that if the zero-field interaction is sufficiently dominant over... 

The one-electron equations (60) offer a new possibility for finding the optimal NSOs by iterative diagonalization of the Fockian, Eq. (66). The main advantage of this method is that the resulting orbitals are automatically orthogonal. The first calculations based on this diagonalization technique has confirmed its practical value [81]. 

For atomic structure calculations, the four-component MCSCF approach was the method of choice for a long time. The implementation of methods for treating very large CSF spaces, particularly Davidson-type diagonalization techniques, produced a tool to compete with highly precise experimental measurements. The coupled-cluster method—or MBPT approach as it is usually called in the physics community—turned out to be a valuable, alternative, size-consistent method. 

The overlap matrix S is also taken into account in the EHT version of the general eigenvalue equation (7) which can be solved by applying the mentioned orthogonal-ization transformation and matrix diagonalization techniques. Due to the independence of Feht from the orbital coefficients, no SCF procedure has to be performed. This is similar to HMO. 

The exact diagonalization method has been widely exploited in the study of polyenes as well as small conjugated molecules. It has also been employed in studying spin systems and systems with interacting fermions and spins such as Kondo lattices. These studies have been mainly confined to low- dimensions. The exact diagonalization techniques also allow bench-marking various approximate many-body techniques for model quantum cell Hamiltonians. 

Hais, 1. M. (1970). Diagonal techniques. Introductory remarks. J. Chromatogr. 48 200-206. 

The analytical solution of Eq. (31) can be obtained using the diagonalization technique or modal projection (Kreyszig, 2006), This is fully detailed in (Fafard et al., 2001). The specific solution for the uniaxial creep case ( =cr = constant) of a cylindrical sample is... 

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