# Homework #3

*For ph461 and ph561 (same homework this week)*

*Due Friday, October 15, 2010 at 5pm*

#### Reading assignment

Chapter 12 and section 8.14 of R,H&B.

#### Q1: Maclaurin and Taylor expansion (10 pts)

Problem 4.24 (b) and 4.30 (a) of R,H&B

#### Q2: Power series (7 pts)

**a)** Calculate terms up to *r*^2 in the Taylor Series expansion of the Lennard Jones potential. Write the Taylor series as an expansion about *r*_min, where *r*_min corresponds the potential minima.

#### Q3: Fourier Series (10 pts)

12.20 of R,H&B.

#### Q4: Matrices (8 pts)

Consider matrices

**a)** Are *A* and *B* Hermitian?

**b)** Find eigenvalues and eigenvectors of *A*. Are there any degeneracies?

#### BONUS QUESTION (5 pts)

**b)** Problem 4.35 of R,H&B

#### PH505 Students: Reading assignment

Chapter 24 of R, H &B.

#### PH505 Students: Additional Homework Question

24.6 of R,H&B.