# Quantum Mechanics 2 (PHYS*4040)

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

**Term:** Winter 2016

**Instructor:** Eric Poisson

## Details

## General information

### Course description

This is the continuation of Quantum Mechanics I (PHYS*3230). The topics covered in this course include single and interacting spins, systems of distinguishable and indistinguishable particles, time-independent perturbation theory, and the fine structure of hydrogen.

### Lectures and Tutorials

#### Class schedule and location

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

Tuesday and Thursday | 08:30am to 09:50am | Room 017 of the Macdonald Institute (MINS) |

#### Tutorials

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

Alternating Wednesdays | 7:00pm to 9:50pm | Room 204 of Animal Science & Nutrition (ANNU) |

The exact scheduling of the tutorials will be posted on Courselink.

### Assessments

- First midterm

Wednesday 10 February 2016, from 7:00pm to 9:00am, in room 204 of Animal Science & Nutrition (ANNU). - Second midterm

Wednesday 9 March 2016, from 7:00pm to 9:00am, in room 204 of Animal Science & Nutrition (ANNU). - Final examination

Monday 18 April, from 7:00pm to 9:00pm. The location will be posted in due course.

Final examination weighting 40% (Scheme A) or 50% (Scheme B). See below.

### Course website

On Courselink

### Instruction

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

Eric Poisson | 519-824-4120 x53653 | MacNaughton 452 | epoisson@uoguelph.ca |

#### Office hours

Each Monday from 9am to 12am. Alternative arrangements can be made by appointment.

Eric is very much an informal guy, and he prefers to be addressed simply as “Eric”. He does not appreciate being subjected to such pompous titles as Doctor, Professor, or His Gracious. Eric’s field of research is general relativity, including black holes and gravitational waves. For additional details, please consult his research web page.

Graduate Teaching Assistant | Office | |
---|---|---|

John Malcolm | MacNaughton 403 | malcolmj@uoguelph.ca |

### Course resources

#### Required text

- David J. Griffiths, Introduction to Quantum Mechanics (Second edition) (Pearson Prentice Hall, 2005, QC 174.12.G75, ISBN 0-13-111892-7).

#### Recommended text

- C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum mechanics (Wiley, 1977, QC 174.12.C6313).

The book by Griffiths is the same book that is used in PHYS*3230 (Quantum Mechanics I). My lectures will follow the book, but not very closely. An essential aspect of your learning will be to reconcile the material as presented in the book with the material as presented in the lectures.

In my opinion, the book by Cohen-Tannoudji is far superior to Griffiths’, but it is also at a higher level, which makes it unsuitable as the main text for this course. But you will benefit greatly by consulting it from time to time.

### Course content

#### Specific learning outcomes

After taking this course the student will be able to:

- Demonstrate an understanding of the postulates of quantum mechanics.
- Employ Dirac’s notation to describe and manipulate quantum states and operators.
- Demonstrate a practical knowledge of spin as a property of quantum-mechanical particles, and how it relates to total angular momentum.
- Solve quantitative problems involving spin interactions with an external magnetic field, and mutual spin interactions.
- Apply the laws of quantum mechanics to multi-particle systems, including bosonic and fermionic systems.
- Apply the theory of time-independent perturbations to find approximate solutions to quantitative problems in quantum mechanics.
- Demonstrate an understanding of how spin and relativistic effects create a fine structure in the degenerate energy levels of the hydrogen atom.

#### Scope, prerequisites, and expectations

This course is a continuation of PHYS*3230 (Quantum Mechanics I). It focuses mostly on the second half of Introduction to Quantum Mechanics, the textbook by David J. Griffiths. Among the topics covered are spin, identical particles, time-independent perturbation theory, and the fine structure of the hydrogen atom.

The only formal prerequisite for this course is PHYS*3230 (Quantum Mechanics I), and mastery of this material will be taken for granted. The course relies also on a working knowledge of classical mechanics, electromagnetism, and basic mathematics.

This is a demanding course in which you will learn sophisticated methods of theoretical physics. These are useful well beyond the context of this course; quantum mechanics finds applications in virtually all areas of physics, chemistry, and nanoscience. This is physics for grown-ups, and it is imperative that you conduct yourself as a grown-up while taking this course. This means, most of all, taking responsibility for your own education. In practice, this means that you will spend a considerable amount of time outside of class hours teaching yourself the material.

The mastery of physics does not come easily to anyone. You must work hard at it, and the work must be done by you, and no one else. My role as your instructor is to help you in this process. I do not believe, however, that I can truly teach you the material. I can lecture on it, give you an orientation, illustrate the basic ideas, and work through some problems, but all this will not make you learn the material. (This may only give you a false impression that you have learned it.) What you must do in addition is teach yourself, and my role as your instructor is mostly to help you teach yourself. Knowledge and understanding will come from your own efforts; they cannot be directly transmitted from me to you. It is imperative that you come prepared to do your own learning in this course, and be willing to spend the time that this requires.

If you follow this course of action you will do very well in this course. And if you follow this advice in other courses as well, your education in physics will be rock-solid. If, however, you fail to read the textbook, go though the math, do the exercises, or if you rely too much on group work, then you will acquire no useful skills from this course. And if this is your general attitude, your education in physics will turn out to be useless. Physics is challenging. Live up to the challenge!

### Lecture content

- Review of Quantum Mechanics I. Postulates of quantum mechanics. Particle in a box. Harmonic oscillator. Angular momentum. Hydrogen atom. Dirac notation.
- Spin [Section 4.4 of Griffiths]. Discovery. Classical model. Stern-Gerlach experiment. Quantum theory of angular momentum. Spin ½. Spin states. Spin in a constant magnetic field. Spin in a rotating magnetic field: magnetic resonance. Two spins. Interacting spins.
- Multiple particles [Section 5.1 of Griffiths]. Schrodinger equation for many particles. Two particles in a box. Two particles: general theory. Distinguishable versus indistinguishable particles. Bosons and fermions.
- Time-independent perturbation theory [Sections 6.1 and 6.2 of Griffiths]. General theory (nondegenerate and degenerate perturbation theory). Deformed box. Perturbed harmonic oscillator. Stark effect.
- Fine structure of hydrogen [Section 6.3 of Griffiths]. Dimensional analysis. Relativistic corrections to atomic Hamiltonian. Perturbation of the ground state. Fine structure of the first excited state.
- Additional topics. Depending on time, we may cover additional topics among the following: EPR paradox, Bell’s inequality, and quantum teleportation.

### Laboratories

There are no labs for this course.

### Tutorials

Tutorials are held on alternating Wednesdays, from 7:00pm to 9:50pm, in room 204 of Animal Science & Nutrition (ANNU). The exact scheduling of the tutorials will be posted on Courselink.

### Course evaluation

The final mark for the course will be the highest of the two marks calculated under the following two schemes. No other marking schemes will be considered.

Scheme | Assignments | Midterm 1 | Midterm 2 | Final Exam |
---|---|---|---|---|

A | 20% | 20% | 20% | 40% |

B | 20% | 15% | 15% | 50% |

A weekly set of homework problems will be made available on Courselink, each to be returned before class one week later. You are permitted to discuss the homework problems with your colleagues while trying to solve them. However, and this is important, after the discussions you must write up the solutions yourself, independently of anyone else. Copying will not be tolerated. Late assignments will not be accepted, unless special arrangements are made ahead of time (not on the day the assignment is due!).

Assignments provide 20% of the course’s final mark. In marking scheme A, the midterm and final exams account for 20%, 20%, and 45% of the final mark, respectively. In marking scheme B, the midterm and final exams account for 15%, 15%, and 50% of the final mark, respectively.

Both midterm and final exams will be closed-book exams, meaning that you will not be allowed to consult your notes nor any other source of information. You will, however, be provided with relevant material such as a formula sheet. Calculators may be required; only non-programmable pocket calculators are permitted. Personal communication or entertainment devices (such as smart phones or MP3 players) are not permitted during the exams.

## Course Policies

### (Not) Working with other students

All work submitted for grading in this course must be each individual student’s own work. While students are encouraged to share thoughts and ideas prior to writing up the solutions, it is not acceptable to share assignment solutions. The

assignments are not group projects, and it is important that you do not show your final written solutions to other students.

### Getting help

One of the best sources of help is the course’s TA and tutorial instructor. In addition, you can come to Eric’s office hours, or make an appointment for a special meeting at another time.

### Grading policies

Each homework assignment will be returned before class begins on the day the assignment is due. Late assignments will not be accepted, unless special arrangements are made ahead of time. No partial credit will be given to unaccepted assignments.

Both midterm and final exams will be closed-book exams, meaning that you will not be allowed to consult your notes nor any other source of information. You will, however, be provided with relevant material such as a formula sheet. Calculators may be required; only non-programmable pocket calculators will be permitted. Personal communication or entertainment devices (such as smart phones or MP3 players) are now permitted during the exams.

### Course policy on group work

You are permitted to discuss the homework problems with your colleagues while trying to solve them. However, and this is important, after the discussions you must write up the solutions yourself, independently of anyone else. Copying will not be tolerated. Evidence of copying will be considered under the Academic Misconduct section of this document (see below).

### Course policy on electronic devices and recording of lectures

What you do with your laptop, smart phone, tablet, etc, during lectures is your own business, so long as it does not create a distraction for your classmates or the instructor. If such a distraction arises you will be asked to leave the classroom.

Electronic recording of classes is expressly forbidden without consent of the instructor. When recordings are permitted they are solely for the use of the authorized student and may not be reproduced, or transmitted to others, without the express written consent of the instructor.

## University Policies

### Academic Consideration

When you find yourself unable to meet an in-course requirement because of illness or compassionate reasons, please advise the course instructor in writing, with your name, id#, and e-mail contact. See the Academic Calendar for information on regulations and procedures for academic consideration.

### Academic Misconduct

The University of Guelph is committed to upholding the highest standards of academic integrity and it is the responsibility of all members of the University community, faculty, staff, and students to be aware of what constitutes academic misconduct and to do as much as possible to prevent academic offences from occurring.

University of Guelph students have the responsibility of abiding by the University’s policy on academic misconduct regardless of their location of study; faculty, staff and students have the responsibility of supporting an environment that discourages misconduct. Students need to remain aware that instructors have access to and the right to use electronic and other means of detection. Please note: Whether or not a student intended to commit academic misconduct is not relevant for a finding of guilt. Hurried or careless submission of assignments does not excuse students from responsibility for verifying the academic integrity of their work before submitting it. Students who are in any doubt as to whether an action on their part could be construed as an academic offence should consult with a faculty member or faculty advisor.

The Academic Misconduct Policy is detailed in the Undergraduate Calendar.

### Accessibility

The University of Guelph is committed to creating a barrier-free environment. Providing services for students is a shared responsibility among students, faculty and administrators. This relationship is based on respect of individual rights, the dignity of the individual and the University community’s shared commitment to an open and supportive learning environment. Students requiring service or accommodation, whether due to an identified, ongoing disability or a short-term disability should contact Student Accessibility Services (SAS) as soon as possible.

For more information, contact SAS at 519-824-4120 ext. 56208.

### Course Evaluation

The Department of Physics requires student assessment of all courses taught by the Department. These assessments provide essential feedback to faculty on their teaching by identifying both strengths and areas of improvement. In addition, student assessments provide part of the information used by the Department Tenure and Promotion Committee in evaluating the faculty member’s contributions in the area of teaching. You are therefore encouraged to take the evaluation procedures seriously, and to provide feedback about this course and its instructor.

### Drop date

The last date to drop one-semester courses, without academic penalty, is Friday March 11, 2016. For regulations and procedures for Dropping Courses, see the Academic Calendar.