Syllabus for Physics 622 –Fall 2019
(Check here frequently for important announcements related to the course)
Course Description: Title: Introduction to Quantum Mechanics I; Credits: 4; Grade Method: REG/AUD;
Prerequisite: PHYS401 and PHYS402 (or equivalent); Topics: Dirac’s “bra-ket” (vector space) notation for state of a
system; Schroedinger equation, with examples; angular momentum related to rotation (continuous) symmetry;
Instructor: Professor Kaustubh Agashe [Phone: (301)-405-6018; Office (note different building than
lecture): Room 3118 of Physical Sciences Complex (PSC); e-mail: kagashe_at_umd.edu]; Office Hours (note
locations and days carefully): Monday 11 am.-12 pm. and Wednesday 3.00-4.00 pm., both in Rm. 3118 PSC.
(It might be possible to have office hours at other times by appointment.)
Teaching Assistants: Yixu Wang [email: wangyixu_at_terpmail.umd.edu; office: Rm. 3264
of PSC; Phone: (301) 458-9889] and Majid Ekhterachian [email: ekhterachian.majid_at_gmail.com; office:
Rm. 3129 of PSC; Phone: (301) 405-6119]; Office hours: Tuesday 3.30 pm.-4.30 in Rm. 3264 of PSC by
Yixu Wang and Thursday 2.30-3.30 pm. in Rm.3129 of PSC by Majid Ekhterachian.
(It might be possible to have office hours at other times by appointment.)
Lecture Time: 10:00-10:50 am. on Monday and Wednesday; 10.00-11.50 am. (with 10 min. break) on Friday
Lecture Room: Room 1113 of Atlantic Building (# 224)
Required Textbook: Modern Quantum Mechanics by Sakurai and Napolitano (denoted below simply as
Recommended textbook: Exploring Quantum Mechanics by Galitski.
A note on prerequisite: this course assumes that students have had a strong undergraduate background
in quantum mechanics, for example, (roughly) at the level of the courses Phys401 and Phys402 taught here
Mechanics’’ by D. Griffiths.
Homework: The homework assignments (problem sets) will generally be assigned here on Mondays, and
should be handed in class the following Friday or in folder outside Room 3118 of PSC by 5 pm. Late homework will
be accepted at the discretion of the instructor (in particular, a valid documented excuse such a medical problem,
religious holiday, or serious family crisis is required), but not after solutions have been handed out.
No homework will be dropped for any reason. For full credit for any written homework or exam problem,
in addition to the correct answer, you must show the steps/justify your approach as much as possible.
Solutions to homework (and exams) will be posted here.
Exams: There will be one midterm exam, which will be take-home (of approximately 24 hours duration) and
contribute to the final grade for the course. Tentatively, this is scheduled for middle/end of October.The final
exam will also be take-home (over a few days), given during the final exam period around middle of
December. You must take the final exam to pass the course. There will be no make-up for the exams,
unless there is a strong documented excuse (a serious medical problem or family crisis).
Details such as which topics will be covered in each exam, the exact dates etc. will be posted later.
Grade: The semester grade will be based on the homework, one midterm exam (take-home) and the final exam (also take-home) with the following (tentative) weights: one midterm exam: 20%, homework: 50%, final exam: 30%.
Attendance: Regular attendance and participation in this class is the best way to grasp the concepts and
principles being discussed. Please try to attend every class and to read up the relevant chapter(s) of the
textbook before coming to the class.
Some class notes will be posted here.
Academic Honesty: Note that, although you are encouraged to discuss homework with other students, any
work you submit must be your own and should reflect your own understanding. In fact, the main way you will
understand Physics (and thus do well on the exams) is by doing the homework (that too by yourself).
In addition, academic dishonesty, such as cheating on an exam or copying homework, is a serious offense
which may result in suspension or expulsion from the University.
The University of Maryland, College Park has a nationally recognized Code of Academic Integrity,
administered by the Student Honor Council. This Code sets standards for academic integrity at Maryland
for all undergraduate and graduate students. As a student you are responsible for upholding these
standards for this course. It is very important for you to be aware of the consequences of cheating,
fabrication, facilitation, and plagiarism. For more information on the Code of Academic Integrity or the
Student Honor Council, please visit here.
To further exhibit your commitment to academic integrity, please sign the Honor Pledge (which covers
all examinations and Assignments) and turn it in as “Homework 1”:
"I pledge on my honor that I will not give or receive any unauthorized assistance (including
from other persons and online sources) on all examinations, quizzes and homework assignments
in this course."
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tenure and promotion process. CourseEvalUM (go here) will open in mid-December for you
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(TENTATIVE) schedule of Physics 622 topics, exams, and homeworks (if needed, a more detailed
schedule, for example, by chapter-sections, might be posted as part of the “announcements” here roughly
at the beginning of each week; the homework assignments will also indicate the topics being covered in
Homework: typically 1 per week, except during exams weeks (for a total of about 10 for the course)
Midterm exam: take-home, assigned and due (after about 1 day) in middle-to-end of October (exact dates
to be announced).
Final exam: take-home, assigned and due (after about 1 week) around middle-December (exact dates to be
Syllabus (main topics of lectures):
(I). Chapter 1 of Sakurai: Basic formalism/language
· Stern-Gerlach experiment: motivates describing state of a system as a vector (``ket’’)
· Developing bra-ket (Hilbert/vector space) notation
· Measurements: observables as operators in vector space
· Position, momentum operators
· Relating bra-kets to (usual) wavefunction
(II). Chapter 2 of Sakurai: Time evolution of state of system
· “Generalized’’ Schroedinger equation
· Schroedinger (“usual”: state evolves, while operator is fixed) vs. Heisenberg (state fixed, operator time-varying) pictures
· Solving simple harmonic oscillator using operator method
· Schroedinger’s (usual) wave equation, with examples
· Feynman’s path integral approach
· Aharanov-Bohm effect (gauge invariance in electromagnetism)
(III). Chapter 3 of Sakurai: angular momentum systematically
· Relating spatial rotations to angular momentum operators
· Spin-1/2 system (rotation by 2p flips sign of state ket)
· Group theory of rotations/angular momentum
· Eigenvalues/states of angular momentum operator
· Solving Schroedinger’s equation for spherically symmetric potential
· Adding angular momenta
· Bell’s inequality
· Tensor operators
(IV). Chapter 4 of Sakurai: Symmetries
· Continuous symmetry (using rotation as example) gives degeneracies
· On to Discrete symmetries: Parity (space inversion)
· Lattice (“discrete”) translation
(V). (Time permitting) Selected topics from quantum information