Homework #4 (35 pts)

For ph461 and ph561 (Question 1d is for ph561 students)

Due Friday, October 22, 2010 at 5pm

Reading assignment

Chapters 8 and 10.

Q1 Properties of Matrices (15 pts)

Consider the matrices

a) Verify that Trace(AB) = Trace(BA), det(AB) = det(A)det(B).

b) Calculate the commutator [A, B].

c) Calculate the inverses A^-1, B^-1, and (AB)^-1. Show that (AB)^-1 = B^-1A^-1.

Q1 Additional part required for ph561 students

d) Calculate A^2 and infer the expressions of A^(2n) and A^(2n+1). Use these results to calculate the matrix of exp(xA).

Q2 Systems of linear equations (10 pts)

Problem 8.36.

Q3 Calculating the Laplacian of a scalar field (10 pts)

Problem 10.15.

PH505 Students: Reading assignment

Chapter 24.

PH505 Students: Additional Homework Question

Problem 24.10.