Many‐electron operator approach in the solid state theory

F. A. Buot

It is suggested that complex problems in ultrasubmicrometer electronics research may greatly benefit from use of the path-integral technique. The use of the Weyl-Wigner formalism of the quantum dynamics of electrons in solids provides a rigorous and straightforward derivation of the path integral in solid-state physics, both from the single-particle and from the many-body field-theoretical description of electron dynamics, without the need to postulate a priori the isomorphism between quantum operators and c-numbers of the base field. A rigorous construction of the path integral in many-body solid-state band theory necessitates a two-stage Weyl correspondence between quantum operators and c-numbers of the base field, namely, the Weyl correspondence of the base field of ``lattice-space'' particle-dynamical variables and that of the continuum many-body field-dynamical variables.

M. F. Olekseeva, K. D. Tovstyuk

Nam Lyong Kang

Some many-body theories of optical transitions in solids were examined from projection and population criteria. The results showed that state-independent projection methods cannot be applied to electron systems with non-uniform energy spectra. Moreover, neglecting some important terms in a second-order approximation leads to invalidation of the population criterion. In addition, a valid theory satisfying these two criteria can be obtained using a proper state-dependent projection operator and Kang-Choi reduction identity, and the result can be interpreted using a diagram, which can model the quantum dynamics of electron in solids.

Helmut Volz, Hermann Haken

M. I. Darby

A brief and simple introduction to the theory of many (N) electron systems that is suitable for undergraduates is given. By considering only three electrons (N = 3) it is possible to write out all the results explicitly. The manipulations of both determinantal wavefunctions and wave-functions in the number representation are considered, and the electron annihilation and creation operators are defined. It is then shown how the Hamiltonian for N electrons is written in second quantized form.

Antonios Gonis