Single-particle theory

Correlated Effective Single-Particle Theory Relativistic Optimized-Potential Method... 

Correlated effective single-particle theory relativistic optimized-potential 227 method... 

Unlike the AT-particle picture, which in principle leads naturally to the exact solution of the many-particle Schrodinger equation, the single-particle picture has led to the development of a number of different approximation schemes designed to address particular issues in the physics of interacting quantum systems. A particularly pointed example of this state of affairs is the strict dichotomy that has set in between so-called single-particle theories and canonical many-body theory[31, 32]. Each of the two methodologies can claim a number of successful applications, which tends to reinforce the perceived formal gap between them. 

The early 3d metals (Sc, Ti, V, and also Ca) are generally considered to be characterized by weak electron correlation in their ground states. Although band-structure theory seems appropriate to describe their excitation spectra, the Ln iii near-edge structures show strong deviations from the prediction of single-particle theory. This is improved by taking into account core-hole-valence electron atomic-like interactions as well as the band structure (5/5). Other XAES spectra of metals are discussed in Section III,B,1. 

Since the TDKS equations (67-72) reproduce the exact nuclear densities, Eq. (76) yields the exact classical trajectory whenever species A contains only one nucleus. When species A contains more than one nucleus we have a system of indistinguishable particles and then, strictly speaking, the trajectories of single nuclei cannot be told apart Only the total density (R, t) and hence the center-of-mass trajectory of species A can be measured. In this case, trajectories of single nuclei can be defined by Eq. (76) within some effective single-particle theory. TDKS theory is particularly suitable for this purpose since the TDKS partial densities lead to the exact total density n. ... 

Here G /" denotes the retarted or advanced Green s function of the central region, while r depends on the surface density of states of the leads and the molecule-lead coupling. Both terms are directly amenable to a first principles evaluation using effective single-particle theories like Hartree-Fock or density functional theory (DFT). In this way the actual electronic structure of the device is accounted for, without the need to resort to few level models for the molecule or empirical wide band approximations for the leads. 

In view of the failure of the rigid sphere model to yield the correct isochoric temperature coefficient of the viscosity, the investigation of other less approximate models of the liquid state becomes desirable. In particular, a study making use of the Lennard-Jones and Devonshire cell theory of liquids28 would be of interest because it makes use of a realistic intermolecular potential function while retaining the essential simplicity of a single particle theory. The main task is to calculate the probability density of the molecule within its cell as perturbed by the steady-state transport process. 

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