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Hey,

I'm having some trouble understanding why the energy changes here between the blue and red paths (see attached image), it's representing state of an electron in a square lattice crystal. Like mathematically I can see it because obviously plug and chugging the different values k in E(k) give different energies but the physics I'm completely lost on. My thinking was that the energy curves would be equal as everything should be.. periodic, I mean we're just in another '1st' Brillouin zone with the other point as a reference.

Obviously it's not the case though unless maths started lying. What am I actually looking at with E(k - G), like what does the translation actually mean physically? We have all the possible states represented in the first Brillouin zone with the allowed k's there, so what am I looking at with k vectors outside the first Brillouin zone?

Thanks in advance, having a hard time wrapping my head around reciprocal space. Not using the template as the question was "find the energies" which I have, I just can't interpret them.

I'm having some trouble understanding why the energy changes here between the blue and red paths (see attached image), it's representing state of an electron in a square lattice crystal. Like mathematically I can see it because obviously plug and chugging the different values k in E(k) give different energies but the physics I'm completely lost on. My thinking was that the energy curves would be equal as everything should be.. periodic, I mean we're just in another '1st' Brillouin zone with the other point as a reference.

Obviously it's not the case though unless maths started lying. What am I actually looking at with E(k - G), like what does the translation actually mean physically? We have all the possible states represented in the first Brillouin zone with the allowed k's there, so what am I looking at with k vectors outside the first Brillouin zone?

Thanks in advance, having a hard time wrapping my head around reciprocal space. Not using the template as the question was "find the energies" which I have, I just can't interpret them.