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Engineering Physics by S. Mani Naidu

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5.5 Quantum free electron theory of electrical conduction

Sommerfeld (1928) applied the principles of quantum mechanics to classical free electron theory.

According to classical theory, the free electrons in a metal have random motions with equal probability in all directions. But according to quantum theory, the free electrons occupy different energy levels, up to Fermi level at 0 K. So, they possess different energies and hence they possess different velocities. The different velocities of these free electrons of a metal can be seen in velocity space. At 0 K, the electrons present in Fermi level possess maximum velocity, represented as VF . We assume a sphere of radius VF , at the origin of velocity space as shown in Fig. 5.5a. Each point inside ...

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