Quantum Mechanics II (PHYS*4040)

Code and section: PHYS*4040*01

Term: Winter 2015

Instructor: Liliana Caballero


Course Information

Pre-requisites: Quantum Mechanics I- PHYS 3230

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

Class Schedule

Day Time Location
Tuesday and Thursday 8:30 a.m to 9:50 a.m  


Lecturer Office Email
Liliana Caballero MacN 330 ocaballe@uoguelph.ca

Office hours

Tuesday from 11:30 a.m to 1:30 a.m (or by appointment).

Course Materials


  • David J. Griffiths, Introduction to Quantum Mechanics, Second edition, Pearson Prentice Hall 2005.

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.
  • Scattering (If time allows). Partial-wave phase shifts.


There will be two midterms and one final exam. They will be closed-book exams.

We will also have weekly homework. The assignments should be returned a week after they are posted. Later assignments will not be accepted unless special arrangements are made ahead of time. A marker will be responsible for marking the homework assignments. Note that although you are permitted to discuss the homework problems with your classmates, you must to 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 the highest of the two marks calculated under the following two schemes. No other marking schemes will be considered.

Scheme Assignments First Midterm Second Midterm Final Exam
A 10% 25 % 25 % 40 %
B 10% 30% 30% 30%
  • First midterm date and time: Thursday February 12th 2015 from 8:30 a.m to 9:50 a.m, in class
  • Second midterm date and time: Thursday March 12th 2015 from 8:30 a.m to 9:50 a.m, in class
  • Final exam date and time: Friday April 17th 2015 from 7:00 p.m to 9:00 p.m, place TBA.

Course Policies

Course Policy regarding use of electronic devices and recording of lectures

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.

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


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 the Centre for Students with Disabilities as soon as possible.

For more information, contact CSD at 519-824-4120 ext. 56208 or email csd@uoguelph.ca or see the university website on Accessibility.

Course Evaluation Information

Please refer to the Course and Instructor Evaluation Website

Drop date

The last date to drop one-semester courses, without academic penalty, is March 6, 2015. For regulations and procedures for Dropping Courses, see the Academic Calendar.