Wave eqtion of electron in a periodic potential

[JayKo]

quoted from Kittel text 8th edition page 170,171
the potential energy is U(x)=$$\Sigma$$$$U_{G}e^{iGx}$$

but why it is also equal to-> U(x)=$$\Sigma$$$$U_{G}e^{iGx}+e^{-iGx}$$


from text explanation, i couldn't get it why there is an extra term of $$e^{iGx}$$

any 1 care to enlight me on this? thanks.

 

[torehan]

quoted from Kittel text 8th edition page 170,171
the potential energy is U(x)=$$\Sigma$$$$U_{G}e^{iGx}$$

but why it is also equal to-> U(x)=$$\Sigma$$$$U_{G}e^{iGx}+e^{-iGx}$$


from text explanation, i couldn't get it why there is an extra term of $$e^{iGx}$$

any 1 care to enlight me on this? thanks.

There is an extra term e^-iGx to make potential energy U(x) a real function.