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Unformatted text preview: (8x8) identity matrix. Problem 2: Consider an infinitely long linear 1-D lattice (lattice constant: a) with one s-orbital per atom (assumed orthogonal) and having a site energy of ε , so that the Hamiltonian looks like <-- a --> Lessons from nanoelectronics: Copyright 2010 [email protected] All Rights Reserved 2 H te i te i te i te i te i Find the dispersion relation E(k). Problem 3: In class we have seen that an infinitely long linear 1-D lattice (lattice constant: a) with a Hamiltonian H t t t t t has a dispersion relation E ( k ) 2 t cos ka where ka (1) Do the same problem using a unit cell of two atoms (instead of one) and show that E ( k ) 2 t cos ka where /2 ka /2 (2) Are (1) and (2) equivalent? Explain....
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This note was uploaded on 11/29/2010 for the course ECE 453 taught by Professor Supriyodatta during the Spring '10 term at Purdue University-West Lafayette.
- Spring '10