PHYSICS 438a: Introduction to Quantum Mechanics

COURSE INFORMATION
Spring 2024
Course Description
Physics 438a is the first course in the introductory quantum mechanics series. It covers the
foundations of quantum mechanics, including the basic postulates, the Schrödinger equation, the
Born rule, Dirac notation and quantum mechanical formalism, exactly-solvable problems in 1 and
3 dimensions, spin, and identical particle statistics.

Learning Objectives
By the end of this course, you should be able to: describe the basic postulates of quantum
mechanics; solve the 1D and 3D particle in a box and harmonic oscillator; solve the hydrogen atom
in 3D; formally prove the uncertainty principle, Ehrenfest’s theorem, and the canonical
conjugation relations; and treat spin, angular momentum, and identical/distinguishable particles
correctly in quantum systems.

Course Instructor
Prof. Eli Levenson-Falk (he/him)
Email address: elevenso@usc.edu
Office: SSC 222
Student hours: Mondays 3:00-4:00 pm and by appointment, both in-person and Zoom

Textbook
Introduction to Quantum Mechanics 3rd Edition, by David J. Griffiths and Darrell F. Schroeter
(Earlier editions of the same book are acceptable, but you may need a classmate’s help to get
problems assigned from the 3rd edition)

Course Logistics
This course is taught as a flipped classroom, which may be different from what you’re used to.
Here’s how it works:
• New concepts will be introduced in short pre-recorded video mini-lectures. I will
post these ahead of time and you can watch them at your convenience, but you must
watch the mini-lecture on a topic before we cover that topic in class.
• You must read the textbook sections we’re going to cover before we cover them. So
please read the textbook and watch the mini-lectures before coming to class. I’ll send
regular updates about which topics we’re about to cover.
• Class time will be divided into 3 parts: worked examples, Q&A, and group work.
 We’ll play around with the ideal order and how much time to give each section, but there
will be no traditional lecture. Instead, I will work out an example or two on the topics of
the day; we’ll have open question & answer time (with open discussion) focused on these
topics; and we’ll split into smaller groups for group work. The group work may include
some work on problem sets. I will be moving between groups to discuss, give advice, and
answer questions.
• Problem sets will be longer and harder than a usual course, but partially done in
class and mostly done in group work. So there will be a lot of work, but you’ll have
plenty of time to do it and plenty of help to figure things out. The total workload for this
course (watching lecture videos, reading the book, and doing the problem sets) will be
similar to other classes.

Administrativia
A. Prerequisites
Physics 304 is a prerequisite and Math 445 is a co-requisite for this course. Exceptions can be
made in compelling circumstances; please contact the instructor.
B. Disability accommodations
Students who need to request accommodations based on a disability are required to register
each semester with the Disability Services and Programs. In addition, a letter of verification to
the instructor from the Disability Services and Programs is needed for the semester you are
enrolled in this course. If you have any questions concerning this procedure, please contact the
course instructor and Disability Services and Programs at (213) 740-0776, STU 301.
C. Academic Integrity
Students who violate university standards of academic integrity are subject to disciplinary
sanctions, including failure in the course and suspension from the university. Since dishonesty
in any form harms the individual, other students and the university, policies on academic
integrity will be strictly enforced. The academic integrity guidelines can be found in
(i) The Trojan Integrity Guide,
http://www.usc.edu/student-affairs/SJACS/forms/tio.pdf
(ii) The Undergraduate Guide for Avoiding Plagiarism,
http:/www.usc.edu/student-affairs/SJACS/forms/tig.pdf

In plain language: don’t cheat! Don’t copy your answers from online, and especially don’t
post homework or exam problems online. We have ways of determining who posted a
problem, and if we catch you doing it then you’ll be reported to SJACS—no warnings,
no second chances. I promise that you can get an excellent grade in this course if you do the
work—just do the work!
D. Classroom Behavior
Masks will be required at all times, just like every other class. If you need to drink some water
or something, lower the mask, take a sip, and put the mask right back on.
 Any student who wants to learn quantum mechanics belongs in this course. It is the job of the
instructor, the TA, and every student to ensure that this welcoming messages is felt by all
students. Questions, discussion, and general interaction are strongly encouraged at all times.
Hostile or unwelcoming comments or behaviors are always unacceptable and will be addressed
appropriately.
E. Faculty Liaison
All courses in the Department of Physics & Astronomy have an assigned Faculty Liaison to
serve students as a confidential, neutral, informal, and independent resource when they wish
to discuss issues concerning their course without directly confronting their instructor. The
Student Ombudsman for this course is Dr. Jack Feinberg, feinberg@usc.edu, 213-740-1134,
SSC 327. Please note that the Faculty Liaison is a mandatory reporter for certain topics (e.g.
self-harm, sexual assault); if you wish to access truly confidential resources for those
subjects, see the listings under “Support Systems”.
F. Statement for observance of religious holidays
USC’s policy grants students excused absences from class to observe religious holidays:
http://orl.usc.edu/life/calendar/absences/. In this case, please contact me in advance to agree
on alternative course requirements.
G. Support Systems
Counseling and Mental Health - (213) 740-9355 – 24/7 on call
studenthealth.usc.edu/counseling
Free and confidential mental health treatment for students, including short-term
psychotherapy, group counseling, stress fitness workshops, and crisis intervention.
National Suicide Prevention Lifeline - 1 (800) 273-8255 – 24/7 on call
suicidepreventionlifeline.org
Free and confidential emotional support to people in suicidal crisis or emotional distress 24
hours a day, 7 days a week.
Relationship and Sexual Violence Prevention and Services (RSVP) - (213) 740-9355(WELL),
press “0” after hours – 24/7 on call
studenthealth.usc.edu/sexual-assault
Free and confidential therapy services, workshops, and training for situations related to gender-
based harm.
Office of Equity and Diversity (OED)- (213) 740-5086 | Title IX – (213) 821-8298
equity.usc.edu, titleix.usc.edu
Information about how to get help or help someone affected by harassment or discrimination,
rights of protected classes, reporting options, and additional resources for students, faculty,
staff, visitors, and applicants. The university prohibits discrimination or harassment based on
the following protected characteristics: race, color, national origin, ancestry, religion, sex,
gender, gender identity, gender expression, sexual orientation, age, physical disability, medical
condition, mental disability, marital status, pregnancy, veteran status, genetic information, and
any other characteristic which may be specified in applicable laws and governmental
regulations. The university also prohibits sexual assault, non-consensual sexual contact, sexual
 misconduct, intimate partner violence, stalking, malicious dissuasion, retaliation, and violation
of interim measures.
Reporting Incidents of Bias or Harassment - (213) 740-5086 or (213) 821-8298
usc-advocate.symplicity.com/care_report
Avenue to report incidents of bias, hate crimes, and microaggressions to the Office of Equity
and Diversity |Title IX for appropriate investigation, supportive measures, and response.
The Office of Disability Services and Programs - (213) 740-0776
dsp.usc.edu
Support and accommodations for students with disabilities. Services include assistance in
providing readers/notetakers/interpreters, special accommodations for test taking needs,
assistance with architectural barriers, assistive technology, and support for individual needs.
USC Support and Advocacy - (213) 821-4710
uscsa.usc.edu
Assists students and families in resolving complex personal, financial, and academic issues
adversely affecting their success as a student.
Diversity at USC - (213) 740-2101
diversity.usc.edu
Information on events, programs and training, the Provost’s Diversity and Inclusion Council,
Diversity Liaisons for each academic school, chronology, participation, and various resources
for students.
USC Emergency - UPC: (213) 740-4321, HSC: (323) 442-1000 – 24/7 on call
dps.usc.edu, emergency.usc.edu
Emergency assistance and avenue to report a crime. Latest updates regarding safety, including
ways in which instruction will be continued if an officially declared emergency makes travel
to campus infeasible.
USC Department of Public Safety - UPC: (213) 740-6000, HSC: (323) 442-120 – 24/7 on call
dps.usc.edu
Non-emergency assistance or information.

Grading
A. Grading Breakdown
Your final course grade will be based upon three major components: problem sets (30% of
grade), midterm exams (30% of grade), and final exam (40% of grade).
All students in this course will be given the same problem sets, the same midterm, and the
same final exam.
B. Minimum Requirements for Passing the Course
In order to receive a passing grade in the course (D or above), you must contribute to solving
at least 10 problems in class. In addition, you must turn in at least 75% of your problem
sets (not every problem needs to be complete, but something needs to be turned in).
C. Problem Sets
 There will be a problem set assigned every week. I expect that it will take you, in total,
approximately 6 hours to complete the weekly assignment (don’t worry, some of this time will
occur in class). These problem sets are the central way you will learn physics. Understanding
physics does not mean knowing the words, having read the book. Instead, understanding
implies having developed the ability to solve physics problems you have not seen before.
Problems will range from the trivial to the difficult. Experience shows a strong positive
correlation between effort on problem sets and success as a student and as a physicist. So do
the assignments and do them honestly.
The counsel to do your own work does not mean that you cannot work with other students
in the class. On the contrary, I encourage students to work together in deciding how to solve
problems. Of course, working together does not mean simply copying solutions from each
other. That action is a violation of academic integrity standards. There is, however, a large
difference between simply copying and learning by cooperating. Take advantage of this
opportunity. Work in groups to figure out a problem, and then write up your own solution.
I also understand that many solutions can be found online. However, apart from being an
academic integrity violation, copying pre-existing solutions denies you an essential learning
experience and this will typically result in a poor performance on exams.
Problem sets will be due by Blackboard submission at 11:59pm on Sundays.
Handwritten solutions must be scanned or photographed and uploaded as a single file,
preferably a PDF. Many free apps exist to do this on a smartphone; I recommend CamScanner
for those that use Android phones.
Solutions to the assignments will be posted on Blackboard shortly after the deadline. As
such, late work will NOT be accepted. However…
I know that a student may find it impossible to complete a specific assignment owing to
illness or other outside commitments. In order to address this issue, before computing your
problem set grade I will automatically discard your two lowest problem set scores. This
will happen automatically, without any special permission, and no notice or documentation
will be required. This is intended to cover things like, but not limited to, illness, intercollegiate
competitions (both academic and non-academic), intramural competitions, conflicts with other
courses scheduling required activities outside of their declared times, and family emergencies.
The only exceptions are: (i) Religious observances when documented on the web site of the
Office of Religious Life, http://orl.usc.edu, in which case any affected student must inform
his/her instructor of the situation no later than the day before the religious observance; (ii)
Extended and well-documented medical issues.
Warning: You should view the fact that the lowest two grades will be dropped as a safety
net, and not as an excuse to goof-off on early assignments. A student who misses an early
assignment for inadequate reasons, and then misses later work for completely legitimate
reasons will receive little sympathy. You do not need to request that specific problem set
grades be dropped, I will just drop the lowest two automatically.
It is very important that your written solutions are written legibly with enough details so
that anybody, not just you, can understand what is going on. Specifically, be sure to show
intermediate steps and use words, not just equations, to explain the solution. Essentially,
 the solution should make sense to someone who knows the material but has never seen this
particular problem before. A solution consisting of a string of equations with no comments, a
figure if required, or some minimal explanation will be considered unsatisfactory and graded
accordingly.
The minimum threshold 75% submission rate cited in the grading criteria above applies to
the assignment as a whole, not to the individual problem count. A partially completed
assignment will satisfy the requirement of submission but, for it to count, there must be some
evidence of attempts at the assigned problems.
D. Examinations
There will be two Midterm Examinations (tentatively scheduled March 1, in class). The
midterm exam will last 100 minutes and will be given during the normal class period.
You will be allowed plenty of reference / study materials during the exam. Don’t worry
about memorizing equations; focus your efforts on understanding concepts.
Students with special examination requirements as documented by the Office of
Disability Services must present their documentation to their instructor as soon after the
start of classes as is possible, and certainly no later than seven calendar days prior to the first
midterm, or as soon as the accommodation is granted.
The final exam for this course will be 2 hours and will be held on Tuesday, May 7 from 11
am – 1 pm. It will be cumulative and cover all topics in the course, but will focus more on the
second half of the course. Plenty of reference materials will be allowed as with the midterms.
Assistance
You have a variety of opportunities for assistance available to you. Here are just some of them:
A. Classroom time
Don’t underestimate the value of questions during the scheduled class period. Many
students are reluctant to pose questions that they fear may seem silly to either their peers or the
instructor. This probably includes you. Almost always, if one student asks a question, there are
several others who have been bothered by the same thing. Often such questions tell me what
is not clear to the students. Stopping and getting everyone together on the issue is much more
useful than simply letting an explanation continue without clarification.
Classroom hours will consist mainly of group problem solving work, Q&A sessions,
demos, and illustrative examples. Introduction of new material will mainly be done through
pre-recorded videos and in the textbook.
B. Student Hours
For more personal attention you can come to my open student hours (held in person and
on Zoom). If at all possible, come to the regularly scheduled student hours listed on the
syllabus. However, if your schedule conflicts with this or you need to meet with me privately,
please e-mail me to set up an appointment. Unfortunately, I cannot schedule private meetings
for problem set help—I’d love to, but there are just too many students!
C. Study Groups
 One of the most effective ways to learn new material is to teach it to others. To this end, I
encourage you to work together in learning the material and in doing problem sets. I encourage
you to discuss problems, approaches to solutions, and even solutions, though you are cautioned
not to simply copy solutions.
You might find it useful to use the Slack channel to set up and organize discussion groups.
D. Published Solutions
Solutions to all problem sets will become available at any time after you have submitted
them for grading. Looking back through the assignments and reminding yourself how to solve
the problems is an excellent way to study. I will also work through examples in recorded videos
and during live classroom time, and will publish the solutions.
E. Other Books
There is no shortage of alternatives to the assigned textbook. Some of these will be in
Leavey Library including:
• Sakurai and Napolitano, Modern Quantum Mechanics
• Shankar, Principles of Quantum Mechanics
• Thayer, Modern Introductory Quantum Mechanics with Interpretation

Electronic Assistance
A. E-mail
E-mail should be used for scheduling meetings, policy questions, signing forms, etc..
Important: Use your USC email account. Non-USC accounts cannot be authenticated and
cannot be relied upon for any grade-affecting communication. Email from non-USC accounts
may be blocked, deleted, or ignored. Your email subject must include “[Physics 438a]”
(including the brackets), followed by the subject of the message. I receive a lot of spam
from textbook companies, so it can be impossible to correctly categorize messages; e-mails
which do not include this subject may be ignored.
I will answer e-mail within 48 hours (usually faster), except on weekends, and will answer
almost any question except “How do I do this problem?” For problem set help, use any of the
other resources listed here! General physics questions or clarifications of an assignment are
ok, but I would prefer you use Slack; occasionally a question cannot be answered easily in e-
mail, in which case you will be asked to come to student hours.
B. Slack Channel
I’ll be conducting most course communication (announcements, Q&A, general discussion)
via the course Slack channels. You will receive important announcements on Slack and
not e-mail, so pay attention to the course Slack channel! I highly encourage you all to
openly discuss concepts, problems, and any general topics you would like. You can even
make a students-only channel and shut me out of it so that you can make fun of my terrible
jokes in peace.
B. Course Web Site
 Everyone registered in PHYS 438a should find a courses already set up within their
Blackboard account (https://blackboard.usc.edu). In this lecture course you will find a copy of
the syllabus, assignments, important news and announcements, and solutions to problem sets
and exams.

SCHEDULE
WEEK TOPICS READING NOTES
1 (Jan 8) History of QM; the basic postulates; Griffiths Why quantum? How
Schödinger equation and wave functions; Ch. 1 do the basics work?
probability; position and momentum;
uncertainty principle

2 (Jan 15) The time-independent Schrödinger Griffiths Let’s start solving

equation; particle in an infinite square Ch. 2.1-2.2 things
well
3 (Jan 22) Quantum harmonic oscillator Griffiths The best, really, just
Ch. 2.3 my absolute favorite
4 (Jan 29) Other exactly-solvable problems in 1D Griffiths The simplest
Ch. 2.4-2.5 problems, which is
why we do our best
to only ever solve
these ones
Midterm Exam, Feb 6, in class
5 (Feb 5) Vector spaces; eigenstates and Griffiths The advanced math
eigenvalues; linear algebra Appendix A that’s actually much
easier than the
“basic” calculus
6 (Feb 12) Hilbert space; observables; eigenstates; Griffiths The FORMALISM
measurement Ch. 3-3.4 (ooooooh)
7 (Feb 19) The uncertainty principle; commutation Griffiths Formalism
relations; operators; Dirac notation Ch. 3 continued; what all
(remainder) the funny arrows
mean
8 (Feb 26) Time evolution; unitary operations; TBA A bit of what I work
quantum computing on
Midterm Exam, Mar 5, in class
9 (Mar 4) The Schrödinger equation in 3D Griffiths We don’t live on
Ch. 4.1 lines…
Spring Break, March 11 - 15
11 (Mar 18) The hydrogen atom, angular momentum Griffiths Here’s why
Ch. 4.2-4.3 chemistry works
12 (Mar 25) Spin, addition of angular momenta, Griffiths Just wait until you
electromagnetic fields Ch. 4 see what the vector
(remainder) potential has been up
 to while we were
distracted
13 (Apr 1) Identical particles, atoms, and solids Griffiths Ever wondered why
Ch. 5 stars aren’t all black
holes?
14 (Apr 8) Translations; conservation laws; parity Griffiths Cool tricks you can
Ch. 6-6.4 play to bring Nöether
into the 20th century
15 (Apr 15) Rotations; degeneracies; selection rules Griffiths Tricks for the future
Ch. 6
(remainder)
16 (Apr 22) Review
Final Exam: Tuesday, May 7, 11 am