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A model calculation of conduction bands and related quantities for simple metals

Expressions for energy bands and some related properties for metallic crystals have been derived by using coherent quantum statistical superpositions of single electronic Bloch waves. The theoretical treatment is carried out by constructing first weakly localized wave packets as a statistical superposition of the Bloch waves at temperature T. These wave packets are then used to build LCAO-like crystalline Bloch states for the conduction electrons. As a detailed application, the expressions for energy bands and for momentum density are given to the free-electron-like system. In the continuum limit of a crystal lattice, the discrete sums appearing in the expressions of various quantities are transformed into integrals, and the general results obtained for "free electrons" are reduced to those of the usual free electron model at the absolute zero of temperature.