Wave eqtion of electron in a periodic potential

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SUMMARY

The wave equation of an electron in a periodic potential is defined by the potential energy function U(x) = ΣU_{G}e^{iGx}. An additional term, e^{-iGx}, is included to ensure that U(x) remains a real function. This is crucial for the physical interpretation of the potential energy in quantum mechanics, as real potentials correspond to observable quantities. The discussion references Kittel's "Introduction to Solid State Physics," 8th edition, specifically pages 170-171, which clarifies the mathematical necessity of this term.

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

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


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

any 1 care to enlight me on this? thanks.
 
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JayKo said:
quoted from Kittel text 8th edition page 170,171
the potential energy is U(x)=[tex]\Sigma[/tex][tex]U_{G}e^{iGx}[/tex]

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


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

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.
 

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