Before reading Bloch theorem i read something to get a feeling to what happens to the energy of electron in a periodic potential, in short what i read said:(adsbygoogle = window.adsbygoogle || []).push({});

Assuming we have a weak periodic potential from -π/a to π/a for example cos(2πx/a), we can write the electron wave function as: α|k>+β|k'>.

my first question is: does this notation mean that the electron is in superposition state of two states, first one being the electron didn't scatter and the second being the electron did scatter?

After that i went on to read Bloch theorem, he stated that the waving function can be written as:

Σu_{k}e^{ikr}. and using Fourier series

Σα_{k-G}e^{i(k-G)r}.

my second question is: correct if I'm wrong but since there is no difference between k and k-G in term of energy does that mean that they are the same state? what does the wave function exactly tell us about the electron? for example what does

α_{k-G1}e^{i(k-G1)r}+α_{k-G2}e^{i(k-G2)r}mean?

sorry for the long question I'm just have a hard time trying to connect the dots

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# I I need help understanding the meaning of Bloch waves

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