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;

discrete symmetries

**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

“Sakurai”)

**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

(see for typical syllabi here and here),
based (for example) on the textbook “Introduction to Quantum

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, pleasesign 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."

**Course Evaluations: **`Your participation in the evaluation of
courses through `CourseEvalUM` is a `

`responsibility you` `hold as a student member of our academic
community. Your feedback is `

`confidential and important to the
improvement of teaching and learning at the University as well as to the `

`tenure and promotion process. `CourseEvalUM` (go here) will open in mid-December for you `

`to complete your ``evaluations for Spring semester courses.
By completing all of your evaluations each `

`semester, you will have the privilege of
accessing the summary reports for thousands of courses online at `

Testudo`.`

**(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

lectures.).

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

announced).

**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

·
Time-reversal

(V). (Time
permitting) Selected topics from quantum information