A Kinetic Energy of Free Electrons

The total energy of a free electron, i.e., one for which — 0, is simply its kinetic energy or 

Combining this equation with Eq. (2.25), it follows that 

In other words, the wave number of an electron is directly proportional to its momentum. Combining these three equations, it follows that for a free electron 

Note that in the presence of a periodic field, the electron s energy can have nonzero values despite that fact that its velocity could be zero. 

Calculate the third ionization of Li. Explain why this calculation can be carried out exactly with no approximations required. 

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