HW4 - symmetry). Compare this to the bandstructure of...

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1. Using a matrix eigenvalue/eigenvector solver such as Matlab, construct the Hamiltonian and calculate at least 5 bands of the 1-dimensional bandstructure and BZ-edge wavefunction probability densities for the potential V(x)=0.5*cos(2 π x/a)(as in lecture 18, p. 3). [Matlab hint: use diag() for matrix construction] 2. Calculate at least 4 bands of the “nearly-free electron” bandstructure for a. the 2D square lattice along Γ -X-M- Γ (see lecture 19, p. 1) b. the 3D FCC lattice along L- Γ -X-U,K- Γ (note that U and K are equivalent by translational
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Unformatted text preview: symmetry). Compare this to the bandstructure of Aluminum in e.g. Rev. Mod. Phys. 30, 102 (1958) or Phys. Rev. 118, 1182 (1960). 3. Consider the (nonprimitive) 3D lattice vectors g G uU , g u u u , and g u . This lattice has a basis G g G , g G g g , and g G g g . Determine the primitive lattice and basis vectors....
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