Show for a simple square lattice that the kinetic energy of a free electron is higher at the corner of the first zone than at the midpoint a side face by a factor of 2.
The Attempt at a Solution
I think I know how to solve, but I am not completely sure I understand the question. The position of the electron refers to the position of its k-vector in k-space right? Well this is not real space, and I can't really see how this has anything to do with the lattice being square in real space.