Quantum Mechanics I (PHYS*3230)
Code and section: PHYS*3230*01
Term: Fall 2023
Department of Physics
College of Engineering and Physical Sciences
PHYS*3230: Quantum Mechanics I
Fall 2023 (LEC:4) [0.50]
This course consists of a formal treatment of quantum mechanics. Topics include wave packets and free particle motion, the Schrodinger equation, harmonic oscillator, piecewise constant potentials, central forces and angular momentum, and the hydrogen atom.
For Course Instructor, Class Time and Location, please check CourseLink.
There are no tutorials for this course.
There are no labs for this course.
Please check CourseLink.
Please check CourseLink.
Final exam weighting
40% (Scheme A) or 45% (Scheme B); see below.
This is a formal course on quantum mechanics, which covers fundamentals like the Schrödinger equation, the probabilistic interpretation of the wave function, and the linear algebra of quantum operators, as well as applications like the simple harmonic oscillator and the hydrogen atom.
In addition to the formal prerequisites for this course [(1 of MATH*1160, MATH*2150, MATH*2160), (MATH*2170 or MATH*2270), (PHYS*2340 or PHYS*2470)], you will be expected to master basic mathematical methods such as those covered in PHYS*3130 (Mathematical Physics). This will be achieved either by taking the course concurrently with PHYS*3230, or by self-study.
This is a demanding course in which you will learn one of the foundational theories of physics: quantum mechanics. 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, and illustrate the basic ideas, 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 instead 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 the 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. Physics is challenging. Live up to the challenge!
Lecture, tutorial, and assignment schedule
The following table provides a very rough guide of the material covered during each week of the semester, as well as key information regarding deadlines. All dates are tentative; check Courselink regularly to get the most updated information. Regular attendance at lectures is the best way to ensure that you are up to date on the relevant course material.
|0: Sept 8||Early quantum ideas||N/A|
|1: Sept 11, 13, 15||Early quantum ideas||N/A|
|2: Sept 18, 20, 22||Schrödinger’s equation||N/A|
|3: Sept 25, 27, 29||Born’s probabilistic interpretation||Assignment 1|
|4: Oct 2, 4, 6||Linear algebra||N/A|
|5: Oct 11, 13||Linear algebra||Assignment 2|
|6: Oct 16, 18, 20||Simple harmonic oscillator I||N/A|
|7: Oct 23, 25, 27||Simple harmonic oscillator I||Midterm exam|
|8: Oct 30, Nov 1, 3||Simple harmonic oscillator II||Assignment 3|
|9: Nov 6, 8, 10||Hydrogen atom||N/A|
|10: Nov 13, 15, 17||Hydrogen atom||N/A|
|11: Nov 20, 22, 24||Angular momentum||Assignment 4|
|12: Nov 27, 29, Dec1||Angular momentum||N/A|
After succeeding this course the student will be able to:
1- Understand the breakdown of classical mechanics in the atomic realm and the emergence of new quantum ideas.
2- Formulate Schrödinger’s equation for a quantum system.
3- Provide a probabilistic interpretation to the quantum wave function and perform calculations of statistical averages.
4- Master elements of abstract linear algebra and apply them to quantum mechanics.
5- Solve the Schrödinger equation for a simple harmonic oscillator.
6- Solve the Schrödinger equation for the hydrogen atom.
7- Apply the quantization rules to angular momentum.
The final mark for the course will be the highest of the two marks calculated under the following schemes A and B. No other marking schemes will be considered.
A set of four homework assignments will also be made available on Courselink, to be returned before the assigned due date, in class. Failure to submit the assignment at that time will result in an automatic 20% penalty, and an additional penalty of 20% per day will apply. No assignment will be accepted after it has been marked. Special arrangements for late submission without penalty require a good reason and must be made well ahead of time.
The midterm and final exams are 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 a formula sheet. Calculators may be required; only non-programmable pocket calculators are permitted. Personal communication or entertainment devices are not permitted during the exams.
(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 solutions to homework assignments, 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.
Completing assignments is an essential part of your preparation toward midterm and final exams. A serious attempt to do the work yourself, independently of others, will provide you with a very good preparation. Relying too much on others to provide pieces of solutions will give you a very poor preparation. Be wise.
Please consult with Eric whenever the need arises. Do not wait too long before getting the help you need; it may be too late by then.
The required textbook is
- David J. Griffiths and Darrel F. Schroeter, Introduction to Quantum Mechanics (3rd edition), Cambridge University Press (2018).
This is a standard text for a first formal course in quantum mechanics. My lectures will not follow the book closely, but it is strongly recommended that you have regular access to a textbook for reference and to complement the lectures. It might as well be this one.
You may find it useful to consult these alternative references:
- R. Shankar, Principles of Quantum Mechanics (2nd edition), Kluwer Boston Incorporated (1999).
- C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics, Volume 1: Basic Concepts, Tools, and Applications, Wiley-VCH (2019).
- C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics, Volume 2: Angular Momentum, Spin, and Approximation Methods, Wiley-VCH (2019).
These books are at a slightly higher level than the course, but they are very good and well-worth consulting. The two-volume set by Cohen-Tannoudji is truly outstanding, and were the books I used as an undergraduate student.
See Course Evaluation (Marking schemes), above.
Course policy on group work
See Course Evaluation ((Not) working with other students), above.
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. (The instructor is easily distracted: I don’t want to see you use your phone during class.) 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.
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 Undergraduate Calendar for information on regulations and procedures for academic consideration.
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.
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.
As per university regulations, all students are required to check their uoguelph.ca e-mail account regularly. E-mail is the official route of communication between the University and its students.
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.
The last date to drop one-semester courses, without academic penalty, is 1 December 2023. For regulations and procedures for Dropping Courses, see the Undergraduate Calendar.