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Pract2_sol

# Pract2_sol - ECE495W Practice problems for EXAM II 1 page...

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Unformatted text preview: ECE495W Practice problems for EXAM II 1 page of notes Friday 0ct.27, 2006 1. A molecule (NOT a solid) consists of eight carbon atoms arranged at the corners of a regular octagon of side ‘a’. Assume (1) one orbital per carbon atom as basis function ; (2) the overlap matrix [S] is a (8x8) identity matrix; and (3) the Hamiltonian matrix is given by H n,” = 8 (site energy) H mm = t if n, m are neighboring atoms Hn,m = 0 if n, m are NOT nearest neighbors <__ a __> What are the eight energy eigenvalues in terms of ‘ 8’ and ‘t’ ‘I F: 8+Mwa’g‘a» 2. Suppose electrons have an E(k) relation given by E0?) = w/ m2c4 + h2c2(kx2 + kyz + kzz) (6%) Obtain an expression for the density of states D(E) in terms of the energy E, the volume V and constants like m, c and h. (a) How would you write the energies of the subbands if the electrons are conﬁned in a thin sheet of thickness “W”? (6) Obtain an expression for the density of states of one of the subbands. W 2. 1 ,.E W4C4+ czﬁhﬁri : wL ” ...
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Pract2_sol - ECE495W Practice problems for EXAM II 1 page...

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