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By G. Hutiray, J. Solyom

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Solution (a) In an alternating field, the equation of motion becomes * d / v , m*—(v) + dt m*(v) *—{- = r „ iajtl(Ot eS0e . If we look for a solution (v) = (v)0exp(icot) we have on substitution The classical free electron model 16 Thus (v)0 = e£0/m*(l/r + ico) = e60x(l ~ i(or)/m*(l (b) If we now take the real part only we have As o0 = ne2r/m* and a= j/£ = ne(vy0ei(Ot/£0eia)t. 2). This is a form of the very common Debye equation, which repeatedly appears in a number of branches of physics, (c) It is clear from the above equation that as the frequency co becomes very large, a falls to zero.

Consider now the hypothetical situation in which we remove all the (free) conduction electrons, one each for each atom. ) We will proceed to return these one at a time and see in what energy level subsequent Quantum mechanical free electron model 24 electrons are placed. The rule is that an electron must be in the lowest available energy level but subject to the Pauli principle. Thus the first electron is placed in the nx = 1 level (Fig. 3(a)). The second can also go in this level, but with a different spin state (Fig.

5(6)) arises. As the temperature rises, so the tail of the distribution becomes longer. 18) and this is known as the Fermi-Dirac distribution. e. those governed by the Pauli exclusion principle. 2 Electron density Using Fermi-Dirac statistics and appropriate solutions of Schrodinger's equation we are now in a position to determine the distribution of electrons with energy. The electron density N(E)dE between energies E and E + dE is the product of two totally independent quantities, the density of states D{E)dE between E and E + dE, and the probability of occupation of a quantum state.

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