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Engineering Physics by S. Mani Naidu

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5.10 Velocity and effective mass of an electron

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 (vg) of the associated wave. The group velocity is given by:

images

where ω is the angular frequency (2πν) and K is the propagation vector images 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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