Electrons in the conduction band of a crystal

This section will deal mainly with the second aspect of the problem. 

All considerations depend on the theorem of Bloch (1929), according to which all solutions of (6) are of the form 

The relation of the Brillouin zone to the crystal structure is discussed in many textbooks on solid-state physics (see e.g. Jones 1960, Ziman 1964, p. 12, Ashcroft and Mermin 1976, Chap. 8). 

2 Methods of calculating energy hands 2.2.1 The tight-binding approximation s-bands 

One of the first ways used to calculate approximate solutions of (6) was the tight-binding method Here we consider an array of N potential wells, of which two are shown in Fig. 1.1, and suppose that in each well individually the electrons can have a number of bound states with energies WQiWl9.Wn and with wave functions 0, . 4 n. When the electron is allowed to move from one well to another, a band containing N states is formed from each bound state of a single well. The approximate wave function describing this motion is 

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