Suppose an electron passes along X-direction in a one-dimensional crystal having periodic potentials:

*V*(*x*) = *V* (*x* + *a*)

where ‘*a*’ is the periodicity of the potential. The Schrödinger wave equation for the moving electron is:

The solution for Equation (5.60) is of the form:

*ψ*(*x*) = *e ^{iKx} u_{k}*(

where *u _{k}*(

Equation (5.62) represents periodic function and *e ^{ikx}* represents plane wave. The above statement is known as Bloch theorem and Equation (5.62) is called Block function. The Bloch function has the property:

*ψ*(*x* + *a*) = exp [*ik* (*x* + *a*)] *u _{k}*(

or *ψ*(*x* + *a*) = *Qψ*

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