**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.