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Three problems in Solid State physics

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1. A plane wave in incident upon single atom regular lattice. Calculate the scattered amplitude from all the atoms.

2. For the unit cell vectors given, find the value of alpha, beta and gamma where maximal diffraction will be observed.

3. Define the Brillouin zone and demonstrate that all wave vectors which start from the origin and satisfy the condition for maximum will terminate on the Brillouin zone boundary.

4. For a two dimensiona crystal with its cell vectors given, find the reciprocal lattice and draw it.

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The 7 pages file shows in great detail how to apply first principles to the problems and how to solve them.

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The incoming plane wave is:
(1.1)
It is scattered by the atom at location .
Due to symmetry we assume that the scattered amplitude from each lattice point is the same and proportional to A.
When a plane wave hits the scattering pint, it is reflected with a different wave vector k, so from the atom to point rD, ...

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