Hole formalism

Finally, the term of d does not split and is labelled Migi d is its own hole-equivalent. While there seems to be a lot to remember in Fig. 3-20, all one needs to commit to memory is the ordering for, say, d and d. The hole formalisms -... 

We introduce the generalized normal ordering in various steps, starting with the traditional particle-hole formalism. 

The particle-hole formalism has been introduced as a simplihcation of many-body perturbation theory for closed-shell states, for which a single Slater determinant dominates and is hence privileged. One uses the labels i,j, k,... for spin orbitals occupied in <1> and a,b,c,... for spin orbitals unoccupied virtual) in . 

This result represents the most important advantage of the particle-hole formalism. Many-body perturbation theory (MBPT) consists mainly in the evaluation of expectation values (with respect to the physical vacuum) of products of excitation operators. This is easily done by means of Wick s theorem in the particle-hole formalism. 

The results of the last section, which are essentially a reformulation of the traditional particle-hole formalism for excitation operators, were first presented in 1984 [8]. At that time it was not realized that only two very small steps are necessary to generalize this formalism to arbitrary reference states. Only after Mukherjee approached the formulation of a generalized normal ordering on a rather different route [2], did it come to our attention how easy this generalization actually is, when one starts from the results of the last section. 

W. Kutzelnigg, Quantum chemistry in Fock space. III. Particle-hole formalism. J. Chem. Phys. 80, 822 (1984). 

One of these kinds of relationship is the hole formalism. According to this... 

An alternative picture of the conductivity of the electrons and holes in intrinsic semiconductors is to consider the electrons in the conduction band as migrating, as expected, toward the positive potential, and to consider the holes as discrete, positive charges migrating in the opposite direction. Although electrons are responsible for conduction in both cases, the hole formalism represents a convenient physical picture. 

Although the material contained in this book concerns the theory of many-electron atoms and ions, its many ideas and methods (e.g., graphical methods, quasispin and isospin techniques, particle-hole formalism, etc.) are fairly universal and may be easily applied (or already are) to other domains of physics (nuclear theory, elementary particles, molecular, solid state physics, etc.). 

J. Breidbach, L.S. Cederbaum, Migration of holes Formalism, mechanisms, and illustrative applications, J. Chem. Phys. 118 (2003) 3983 A.I. Kuleff, J. Breidbach, L.S. Cederbaum, Multielectron wave-packet propagation General theory and application, J. Chem. Phys. 123 (2005) 044111. 

Principle of hole formalism according to this principle the equivalence... 

Analysis of the products of field operators in these equations leads to a representation of the wave function and of the level shift in terms of diagrams of the type first introduced by Feynman. These diagrams provide a simple pictorial description of electron correlation effects in terms of the particle-hole formalism. 

The matrix elements of the generators, Sab, can be evaluated using the graphical methods of spin algebra.174-176 The particle-hole formalism introduced by Flores and Moshinsky177 and recently discussed by Paldus and Boyle178 is most suitable for such developments. 

Technetium(II) complexes are paramagnetic with the d5 low-spin configuration. A characteristic feature is the considerable number of mixed-valence halide clusters containing Tc in oxidation states of +1.5 to + 3. This area has been reviewed (42). For convenience, all complexes, except those of [Tc2]6+, are treated together here. EPR spectroscopy is particularly useful in both the detection of species in this oxidation state and the study of exchange reactions in solution. The nuclear spin of "Tc (1 = f) results in spectra of 10 lines with superimposed hyperfine splitting. The d5 low-spin system is treated as a d1 system in the hole formalism (40). 

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