Quantum Mechanics II (PHYS*4040)

Code and section: PHYS*4040*01

Term: Winter 2022

Instructor: Liliana Caballero


Course Information

Class Schedule

Course Component  Day Time Location
Lectures Tuesday/Thursday 1:00 - 2:20 pm ANNU Room 204
Tutorials Wednesday 7:00 - 9:50 pm ANNU Room 204


Name Role Email
Liliana Caballero Instructor ocaballe@uoguelph.ca

Office hours

Wednesday 9 to 10 a.m or email me to arrange an appointment.


Quantum Mechanics I- PHYS 3230

The course also relies on a working knowledge of classical mechanics, electromagnetism, and mathematics.

Class Resources

Required Textbook

  • David J. Griffiths, Introduction to Quantum Mechanics, Second or Third edition, Pearson Prentice Hall.

Recommended texts

  • C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics, Wiley, 1977
  • The University of Guelph Library has a wonderful resource of e-books at Scholars Portal books. You can login in with your University credentials and have access to countless books with problems to practice. As an example, you will find:
    Franz Schwabl, Quantum Mechanics, Springer, 2007.

Course content

Specific learning outcomes

After taking this course the student will be able to:

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

Lecture Content

  • Review of Quantum Mechanics I. Postulates of quantum mechanics. Harmonic Oscillator. Angular momentum. Hydrogen Atom.
  • Spin. Discovery. Stern-Gerlach experiment. Quantum theory of angular momentum. Spin-1/2. Spin in a constant magnetic field. Two spins. Interacting spins.
  • Multiple Particles. Schroedinger equation for many particles. Two particles. Distinguishable vs indistinguishable particles. Bosons and fermions.
  • Time-Independent perturbation theory. Nondegenerate and degenerate perturbation theory. Applications.
  • Fine and Hyperfine structure of Hydrogen Atom. Relativistic corrections to atomic Hamiltonian. Perturbation of the ground state. Fine structure of the first excited state.


There will be one midterm and one final exam. Both are in-class evaluations.

We will also have weekly homework. Return date will be posted in each assignment. Later assignments will not be accepted unless special arrangements are made ahead of time. The Teaching Assistant will be responsible for marking the homework assignments. Note that although you are permitted to discuss the homework problems with your classmates, you must write up the solutions yourself. At this stage of your career you should develop your answers independently of anyone else. Copying will not be tolerated. The homework problems are exercises that give you practice and keep you up-to-date with the course material. However, you need to work on more problems on your own in order to master the content of the course.

The final mark of the course will be calculated with the following scheme. No other marking schemes will be considered.

Assignments Midterm Final Total
20% 40% 40% 100%

Midterm date: Thursday February 17th 2022 in-class
Final exam date: TBA.
Late assignments will be received up to two days later and marked with 20% off. 

University Statements

Email Communication

As per university regulations, all students are required to check their e-mail account regularly: e-mail is the official route of communication between the University and its students.

When You Cannot Meet a Course Requirement

When you find yourself unable to meet an in-course requirement because of illness or compassionate reasons please advise the course instructor (or designated person, such as a teaching assistant) in writing, with your name, id#, and e-mail contact. The grounds for Academic Consideration are detailed in the Undergraduate and Graduate Calendars.

Drop Date

Students will have until the last day of classes to drop courses without academic penalty. The deadline to drop two-semester courses will be the last day of classes in the second semester. This applies to all students (undergraduate, graduate and diploma) except for Doctor of Veterinary Medicine and Associate Diploma in Veterinary Technology (conventional and alternative delivery) students. The regulations and procedures for course registration are available in their respective Academic Calendars.

Copies of Out-of-class Assignments

Keep paper and/or other reliable back-up copies of all out-of-class assignments: you may be asked to resubmit work at any time.


The University promotes the full participation of students who experience disabilities in their academic programs. To that end, the provision of academic accommodation is a shared responsibility between the University and the student.

When accommodations are needed, the student is required to first register with Student Accessibility Services (SAS). Documentation to substantiate the existence of a disability is required; however, interim accommodations may be possible while that process is underway.

Accommodations are available for both permanent and temporary disabilities. It should be noted that common illnesses such as a cold or the flu do not constitute a disability.

Use of the SAS Exam Centre requires students to book their exams at least 7 days in advance and not later than the 40th Class Day.

For Guelph students, information can be found on the SAS website


Academic Integrity

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 encourages academic integrity. 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.

Recording of Materials

Presentations that are made in relation to course work - including lectures - cannot be recorded or copied without the permission of the presenter, whether the instructor, a student, or guest lecturer. Material recorded with permission is restricted to use for that course unless further permission is granted.


The Academic Calendars are the source of information about the University of Guelph’s procedures, policies, and regulations that apply to undergraduate, graduate, and diploma programs.

Academic Calendars



Please note that the ongoing COVID-19 pandemic may necessitate a revision of the format of course offerings and academic schedules. Any such changes will be announced via CourseLink and/or class email. All University-wide decisions will be posted on the COVID-19 website and circulated by email.