Properties of Electron Gas in Constant Magnetic and Electric Fields.
Final technical rept.,
TECHNION RESEARCH AND DEVELOPMENT FOUNDATION LTD HAIFA (ISRAEL)
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Significant progress was made in applying the kq-representation to the construction of localized states and effective Hamiltonians in perturbed crystals. The work started with the developing of a scheme for localized states on perfect lattices. Operators were defined that have as eigenvalues all the discrete vectors of the direct and reciprocal lattices in crystals. The construction of the localized states leads to a quantum mechanical description of the Bravais and the reciprocal lattices. The eigenfunctions of the lattice operators form a complete orthonomal set of localized functions in both the configuration and the Fourier space. In addition, these localized states clarify the structure of the kq-representation. On the fundamental side of the problem a close connection was established between a general set of localized states on a phase plane lattice and the well known von-Neumann coherent states. Localized states in the kq-representation were applied to band calculations and to the dynamics of electrons in perturbed crystals. In the band calculation problem a known variational principle satisfied by Wannier functions was extended to cover free electron-like solids. This extension makes the variational principle applicable to the whole range of solids, from tight binding to free electron-like solids.
- Electricity and Magnetism
- Solid State Physics