University of Kentucky

Department of Physics and Astronomy

PHY 520: Introduction to Quantum Mechanics

Spring 2008

Homework set 1

Due Date: January 18, 2008 (Friday)

1. a. Calculate

b. Calculate the determinant and inverse of

Solution

2. a. With respect to a orthonomal basis (vectors are perpendicular to each other and each vector has unit length), calculate the length of the vector

b. Write down the transpose of this matix.

Solution

3. Consider i, j, and k as the basis of the three dimensional vector space. Now construct a new basis with a=i+j, b=i+k, c=j+k.

a. Construct the change of basis matrix.

b. Write vector r = i+2j+3k in terms of a, b, and c.

c. Convert the following matrix from the old ijk-representation to the new abc-representation:

Solution