495_Pract2 - ’ and ‘t’ 2 Suppose electrons have an...

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1 ECE495W Practice problems for EXAM II 1 page of notes Friday Oct.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 <-- a --> H n , n = ε (site energy) H n , m = t if n, m are neighboring atoms H n , m = 0 if n, m are NOT nearest neighbors What are the eight energy eigenvalues in terms of ‘
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Unformatted text preview: ’ and ‘t’ ? 2. Suppose electrons have an E(k) relation given by E ( G k ) = m 2 c 4 + = 2 c 2 ( k x 2 + k y 2 + k z 2 ) 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 . = How would you write the energies of the subbands if the electrons are confined in a thin sheet of thickness “W”? Obtain an expression for the density of states of one of the subbands....
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This note was uploaded on 02/19/2012 for the course ECE 495w taught by Professor Supriyodatta during the Fall '06 term at Purdue.

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