PHY 520: Introduction to Quantum Mechanics

Spring 2009

Homework set 3

Due Date: February 16, 2008 (Monday)

1. Start from the trivial orthonomal basis for column matrix:

Construct another orthonorma basis b₁, b₂, and b₃. Prove explicitly your choice is orthonormal. Construct the 3´3 matrix U for change of basis between (a₁, a₂, a₂) and (b₁, b₂, b₃) by putting the column matrices of b₁, b₂, and b₃side by side together. Show that U is unitary U⁺=U^-1.

Solution

2. Zettili 1^st edition. Chapter 2. Exercise 2.8.

3. Zettili 1^st edition. Chapter 2. Exercise 2.13.

4. Zettili 1^st edition. Chapter 2. Exercise 2.14.

5. Zettili 1^st edition. Chapter 2. Exercise 2.22.

6. Zettili 1^st edition. Chapter 2. Exercise 2.24.