According to de Broglie hypothesis, a moving electron is associated with a wave. The velocity of an electron (*v*) is equal to the group velocity (*v*_{g}) of the associated wave. The group velocity is given by:

where *ω* is the angular frequency (2*πν*) and *K* is the propagation vector of the wave.

In quantum mechanics, the energy, ‘*E*’ of an electron is given by:

*E* = *ħω* _____ (5.77)

Differentiating Equation (5.77) with respect to ‘*K*’ , we get:

From Equations (5.76) and (5.78), we have:

In quantum theory, ...

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