Physics-432

Homework Set (6)

This homework set is due on Saturday (8^th of Safar) at 10.00 p.m.

If you need help, please e-mail me or visit me in my office.

Please solve fully and clearly, state assumptions, circle final answers, and comment wisely (when applicable).

Do not discuss this homework with your colleagues in any way, shape or form!

Question #1:

Use the Central Equation (7-27) to solve the Kronig Penney model for a ring of unit length and lattice spacing a << 1. The periodic potential U(x) is: (A: constant)

U(x) = A a Sd(x-sa); the sum is over s.

Question #2:

By solving for orbitals with wave-vectors (k) near the zone boundary (in 1-D), show regarding the nearly free electronic model that there is a quadratic dependence of energy on the wave-vector Ҝ = k – G/2. [G: a reciprocal lattice vector]

Question #3:

e-mail me (zhyamani@kfupm.edu.sa) two web-site URLs that describe the nearly free electron model and its prediction of metals and insulators.