9780030839931, Chapter 11, Problem 1P

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Chapter 11, Problem 1P Problem Boundary Conditions on Electron Wave-Functions in Crystals Let r locate a point just within the boundary of a primitive cell C0, and r' another point infinitesimally displaced from r just outside the same boundary. The continuity equations for are lim = 0, lim - = 0. (11.37) (a) Verify that any point r on the surface of a primitive cell is separated by some Bravais lattice vector R from another surface point and that the normals to the cell at r and r+ R are oppositely directed. (b) Using the fact that can be chosen to have the Bloch form, show that the continuity conditions can equally well be written in terms of the values of entirely within a primitive cell: (11.38) for pairs of points on the surface separated by direct lattice vectors R. (c) Show that the only information in the second of equations (11.38) not already contained in the first is in the equation = R + R) + R), (11.39) where the vector n is normal to the surface of the cell. Step-by-step solution There is no solution to this problem yet. Get help from a Chegg subject expert. Ask an expert