# Quantum Mechanics II (PHYS*4040)

**Code and section:** PHYS*4040*01

**Term:** Winter 2010

**Instructor:** Robert Wickham

## Details

## Course Information

### Instruction

Instructor | Office | Phone | |
---|---|---|---|

Rob Wickham | MacN 448 | (519) 824-4120 × 53704 | rwickham@uoguelph.ca |

### Lectures

Day | Time | Location |
---|---|---|

Tuesday and Thursday | 8:30 am – 9:50 am | MacK 310 |

Office Hours: Tuesday, 11 am – 12 pm and Wednesday, 1 pm – 3 pm

### Course Materials

#### Required texts

- David J. Griffiths, Introduction to Quantum Mechanics, 2nd ed. (Pearson Prentice Hall, 2005)
- R. Shankar, Principles of Quantum Mechanics, 2nd ed. (Springer, 1994)

#### Other texts

- R. L. Liboff, Introductory Quantum Mechanics
- J. J. Sakurai, Modern Quantum Mechanics
- E. Merzbacher, Quantum Mechanics
- L. I. Schiff, Quantum Mechanics
- C. Cohen-Tannoudji, B. Diu, and F. Lalo¨e, Quantum Mechanics
- Schaum’s Outlines: Quantum Mechanics
- D. McMahon, Quantum Mechanics Demystified

### Evaluation

Assessment | Weight |
---|---|

Assignments | 30 % |

Midterm test | 20 % |

Essay | 10 % |

Final Exam | 40 % |

Assignments are due weekly. There will be no extensions and all deadlines are hard. The use of Maple (etc.) to do assignment problems or make graphs is forbidden, unless otherwise noted.

Students may discuss problems amongst themselves but their written solutions must not be shared with anyone (this would be an example of plagiarism).

Plagiarism is the act of appropriating the “...composition of another, or parts or passages of his [or her] writings, or the ideas or language of the same, and passing them off as the product of one’s own mind...” (Black’s Law Dictionary). A student found to have plagiarized will receive zero for the work concerned. Collaborators shown to be culpable will be subject to the same penalties.

**Makeup Classes:** I will be away the week of March 15th, and we will need to make up the two missed classes. I propose the following dates for the makeup classes: Monday, January 25th, 7 – 8:30 pm and Monday, February 1st, 7 – 8:30 pm.

**Midterm test date:** Friday, March 5th, 7 – 9 pm

**Draft essay due date:** February 11th, in class

**Essay due date:** March 25th, in class

**Exam date:** Friday, April 16th, 7 – 9 pm

**Medical Certificate:** Required if the exam is missed.

### Course Outline

In this course, students will build on the foundations of Quantum Mechanics I by developing their skills with the mathematics and formalism of quantum mechanics, by solving problems in three dimensions, and by learning how angular momentum is treated in quantum mechanics. Students will also be introduced to perturbative approaches.

#### Part I: Mathematical Structure of the Theory, and Measurement (4 weeks)

Griffiths Ch. 3, Appendix; Shankar Chs. 1, 4

- Measurement and postulates, fundamental problem
- Linear algebra: the language of quantum mechanics
- Structure of state space: subspaces, basis, representation of operators as matrices
- Approach to predict the probabilities for the results of a measurement
- Degenerate subspaces
- Continuous basis: position and momentum representations
- Quantum mechanics in three dimensions, complete sets of commuting observables

#### Part II: Angular Momentum (6 weeks)

1) Orbital angular momentum

Griffiths 4.3; Shankar Ch. 12

- Commutation relations, interpretation, consequences
- Eigenproblem for L2 and Lz, interpretation, consequences
- Eigenproblem in the |nlmi basis
- Eigenproblem in the position basis, measurement outcomes

2) Central potential problem

Griffiths 4.1-4.2; Shankar 12.6, Ch. 13

- Solution of the energy eigenproblem in a general central potential
- The radial and angular equations, energy and length scales
- Application to the hydrogen atom (Coulomb potential)

3) Spin angular momentum

Griffiths 4.4; Shankar Ch. 14

- Experimental observations, algebraic theory for spin, spin state space
- Spin 1/2, spinor representation
- Spin precession in a magnetic field

4) Total angular momentum of a system

Griffiths 4.4; Shankar Ch. 15

- Complete description of a particle with spin and orbital angular momentum
- Direct product spaces
- Multiple particles: Total angular momentum of two spin 1/2 particles
- Addition of angular momentum: general case

#### Part III: Perturbation Theory (2 weeks)

1) Time-independent perturbation theory

Griffiths Ch. 6; Shankar Ch. 17

- The idea of a perturbation, formulation of the perturbation series
- How to compute approximate eigenvalues and eigenvectors
- Degenerate perturbation theory
- Example: the Stark effect in hydrogen