The quantum free-electron gas

The electron is confined not only to certain wavelengths but also to quantised energies,  

The energy of a single electron in a rectangular block of metal with sides of length a, b and c, lying along the three axes x, y and z, is  

As described in Chapter 1, wavefunctions with the same energy are said to be degenerate. Thus, for a cubic container the solutions Hx= riy=,  

The degeneracy means that the number of energy levels within a particular energy range is not a constant but increases with increasing values of k. In order to solve the problem of the electron contribution to the specific heat of a metal it is necessary to discover how many energy levels (i.e. 

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