# Quantum Mechanics II (PHYS*4040)

Code and section: PHYS*4040*01

Term: Winter 2021

Instructor: Liliana Caballero

## Course Information

### Class Schedule

Tuesday and Thursday from 10:00 a.m to 11:20 a.m

### Lecture Room

We will meet have online lectures. We will meet via Zoom. The link to access the meeting will be posted in Courselink.

### Tutorials

Wednesday 07:00PM - 09:50PM

### Instructor

Liliana Caballero
email: ocaballe@uoguelph.ca

#### Office hours

Email me to arrange an appointment.

TBA

### Pre-requisites

Quantum Mechanics I- PHYS 3230

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

### 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 take-home 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 Exam
20% 40 % 40 %

#### Midterm date

Uploaded on Monday February 22th 2021

#### Final exam date

I’ll upload the exam on the week of April 15th 2021.

Late assignments will be received up to two days later and marked with 20% off.

## Course Statements

### Working with others

Physics is not done in a vacuum. (OK, sometimes it is...) Students may discuss assignments 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.

### 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 possible areas of improvement. In addition, annual student assessment of teaching provides part of the information used by the Department’s Tenure and Promotion Committee in evaluating the faculty member's contribution in the area of teaching.

The Department's teaching evaluation questionnaire invites student response both through numerically quantifiable data, and written student comments. In conformity with University of Guelph Faculty Policy, the Department’s Tenure and Promotions Committee only considers comments signed by students (choosing "I agree" in question 14). Your instructor will see all signed and unsigned comments after final grades are submitted. Written student comments may also be used in support of a nomination for internal and external teaching awards.

Note: No information will be passed on to the instructor until after the final grades have been submitted.

## University Statements

### Disclaimer

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.

### Illness

The University will not normally require verification of illness (doctor's notes) for fall 2020 or winter 2021 semester courses.  However, requests for Academic Consideration may still require medical documentation as appropriate.

### E-mail 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 email the course instructor to make arrangements. 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.

### Accessibility

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.

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

The University of Guelph’s primary mode of course delivery has shifted from face-to-face instruction to remote and online learning due to the ongoing COVID-19 pandemic. As a result, some learning activities (e.g., synchronous lectures or student presentations) may be recorded by faculty, instructors and TAs and posted to CourseLink for grading and dissemination; students may be recorded during these sessions.
The following statements may be added to the course outline and it is recommended these are discussed in any synchronous courses during the first week of classes.

By enrolling in a course, unless explicitly stated and brought forward to their instructor, it is assumed that students agree to the possibility of being recorded during lecture, seminar or other “live” course activities, whether delivery is in-class or online/remote.
If a student prefers not to be distinguishable during a recording, they may:

1. turn off their camera
2. mute their microphone
3. edit their name (e.g., initials only) upon entry to each session
4. use the chat function to pose questions.

Students who express to their instructor that they, or a reference to their name or person, do not wish to be recorded may discuss possible alternatives or accommodations with their instructor.

### Online Behaviour

Inappropriate online behaviour will not be tolerated.
Examples of inappropriate online behaviour include:

• Using obscene or offensive language online
• Copying or presenting someone else's work as your own
• Adapting information from the Internet without using proper citations or references
• Buying or selling term papers or assignments
• Posting or selling course materials to course notes websites
• Having someone else complete your quiz or completing a quiz for/with another student
• Stating false claims about lost quiz answers or other assignment submissions
• Threatening or harassing a student or instructor online
• Discriminating against fellow students, instructors and/or TAs
• Using the course website to promote profit-driven products or services
• Attempting to compromise the security or functionality of the learning management system