By von Neumann J.

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**Extra resources for Collected works. Vol.1 Logic, Theory of Sets and Quantum Mechanics**

**Sample text**

Let us now consider trivalent aluminum (Al), which forms a fcc lattice. The first Brillouin zone is entirely filled with electrons. The second zone is half filled with electrons, starting with the zone boundary as shown in Fig. 6. As another example, we examine the Fermi surface of lead (Pb), which also forms a fcc lattice. Since this metal is quadrivalent and hence has a great number of conduction electrons, the Fermi surface is quite complicated. 7. For more detailed description of the Fermi surface of metals see standard texts on solid state physics (Refs.

Thus there is a sharp Fermi surface represented by which separates the electron-filled (low-energy side) from the empty (high energy side). The Fermi surface for a real metal in general is complicated in contrast to the free-electron Fermi sphere represented by The independent electron model with a sharp Fermi surface at 0 K is called the Fermi liquid model of Landau [2]. As we show later, many thermal properties of conductors are dominated by those electrons near the Fermi surface. The shape of the Fermi surface is very important for the occurrence of superconductors.

With the neglect of the spin degeneracy, the number N is equal to the total volume enclosed by the Brillouin boundary divided by unit volume which equals the number of the ions in the normalization volume. It is also equal to the number of the conduction electrons in a monovalent metal. 3. THE FERMI SURFACE 33 Thus, the first Brillouin zone can contain twice (because of spin degeneracy) the number of conduction electrons for the monovalent metal. This means that at 0 K, half of the Brillouin zone may be filled by electrons.

### Collected works. Vol.1 Logic, Theory of Sets and Quantum Mechanics by von Neumann J.

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