Feynman's Messenger Lecture on Quantum Mechanics, Cornell, 1964.
PHY6645: Quantum Mechanics I
This course is the first semester of a two semester graduate level course on
Quantum Mechanics. I will be assuming all in the class have
mastered this subject as taught at the advanced undergraduate
level, for example that of Griffith's textbook.
The goal of the first semester is to
develop the subject systematically, beginning with
a review of the mathematics of linear operators and vector spaces,
in the context of setting out the principles of quantum mechanics as codified
in Dirac's book. We shall also review Hamilton's formulation
of classical mechanics, the structure of which reveals close
parallels with quantum mechanics. In particular, the
concept of canonical transformations in classical and
quantum mechanics will be employed to gain insight into symmetries and their relation to conservation laws.
We then go on to develop
a systematic understanding of the quantum dynamics of
nature. Applications in the first semester will mostly be
limited to the simple systems encountered in undergraduate quantum
mechanics including simple one dimensional problems,
the free particle in three dimensions,
the harmonic oscillator, and the hydrogen atom. Approximation methods
in the first semester will include the WKB approximation
and first order perturbation theory.
PHY6646: Quantum Mechanics II
This course is the second semester of a two semester graduate level course on
quantum mechanics. A detailed treatment of rotational invariance and
angular momentum will be given, including representations
of the rotation group, spin, and the addition of
angular momentum, and the WignerEckart theorem.
The description of identical particles, bosons and femions will
be developed.
We will develop perturbation theory systematically
in both its time independent and time dependent forms. We will
introduce variational methods and employ them to nonperturbative
approximations.
Advanced applications in the second semester will be multielectron
atoms, resonance scattering, inelastic scattering, and
radiative decay.
Below are links to course information, a syllabus, a convention
and formula sheet. As the course develops, I will improve and update
my lecture notes, which will be posted here.
Required text:

R. Shankar ,
Principles of Quantum Mechanics, Second Edition
(Springer Science, New York, corrected printing 2008)
 Erratum: Some versions of our textbook have
a typo in Exercise 1.8.8 (2).
The left side of the displayed equation should be M^iM^j, not
M^iM^i.
Course Information:
Class and contact Information
email: thorn@phys.ufl.edu
Lectures: MWF period 4 (10:4011:30 am), NPB 1101
Optional Discussion Class (math review and more): TBD
Office hours: MWF period 5 (11:45a12:45p), NPB 2069 and by appointment
Our grader: Delaram Ghoreishilangroudi
email: d.ghoreishi@ufl.edu
Office hours: Please email Delaram to set up a meeting about
homework grading. Her physics office is NPB2220.
Announcements, Spring 2017
 The video of Feynman's Messenger Lecture on Quantum Mechanics,
Cornell, 1964 is linked above.
 Generally I would like the homework to be handed in at the
beginning of class on the due date. However, I will accept
without penalty homework handed to me in my office (not in
my mailbox!) before 5pm on the due date.
 Problem set 1 posted 2 January 2017.
 Problem set 2 posted 9 January 2017.
 Solution to holiday problem posted 10 January 2017.
 Lecture notes updated 11 January 2017.
 Problem set 3 posted 16 January 2017.
 Solution set 1 posted 24 January 2017. Apologies for the late posting.
I will post Solution Set 2 after 5pm tomorrow.
 Problem set 4 posted 24 January 2017.
 Problem set 5 posted 31 January 2017.
 Solution set 3 posted 1 February 2017.
 Problem set 6 posted 6 February 2017.
 Solution set 4 posted 8 February 2017.
 Problem set 7 posted 14 February 2017.
 Jake Rosenzweig has narrowed down a time for makeup classes
to Monday at 5:10pm. So far it looks like we will be able to use
room 1220, but I have reserved the seminar room 2165 as backup. I will
be out of town for the three classes in the week following spring break,
and we need another makeup class for those who attended Laura
Greene's seminar. I propose two makeups before spring break on
20 and 27 February, and a third on 20 March.
Please let Jake or me know if 5:10 on Monday conflicts with
your schedule. I will ask a colleague to give one of my missed classes.
 Solution set 5 posted 15 February 2017.
 Solution set 6 posted 23 February 2017.
 To help you review for the midterm, I will post solution set 7
by the weekend. Also, since I will be away for the week immediately following
spring break, I plan to post a combination of Problem Sets 8 and 9, which
will be due on 22 March 2017.
 Combined Problem sets 8/9 posted 24 February 2017. As mentioned,
I will be attending a workshop in Munich during the week following
spring break. This combined problem set covers our work on perturbation
theory and the variational methods applied to helium, most of which
we will have covered in class before spring break. The last problem is a first
one on time dependent perturbation theory which will be the focus of
our regular class on Monday 20 March as well as the makeup class tentatively
scheduled for Monday 20 March at 5:10pm.
 Solution set 7 posted 24 February 2017.
 Lecture notes updated 25 February 2017.
 I have graded the midterm; here are the statistics: Average=73.5;
median=75; Range=5288
 The final makeup class will be next Monday 27 March rather than today.
It will be at 5:10 in room 1220.
 Problem Set 10 posted 21 March 2017.
 Problem Set 11 posted 28 March 2017.
 Solution set 8/9 posted 29 March 2017.
 Problem Set 12 posted 4 April 2017.
 Solution set 10 posted 5 April 2017.
 Faculty Course evaluations will be conducted entirely
on line. They open 8 April 2017
and will continue until 21 April 2017.
These evaluations provide very important feedback,
so it is essential that we all do our best to maximize the number of responses.
You can access the evaluation form at your leisure from the web site:
https://evaluations.ufl.edu/evals/
where you can find instructions and links to a gatorlink login page.
It is probably a good idea if you bookmark the page so you can easily find
it in the future.
 The final Problem Set 13 posted 12 April 2017.
 Solution set 11 posted 14 April 2017.
 The last day I will accept
homework, including all late homework, will be the last day of class,
19 April 2017, 5pm. This means that Problem set 13, due on 19 April will
not be eligible for late submission.
 The final exam will cover all homework and lecture material for
the second semester. Approximately 25% of the final will be on material
before the midterm. The exam formula sheet which will be included
in exam booklets may be
perused here .
 Solution sets 12 and 13 posted 19 April 2017.
 You may pick up graded homework (through Set 12) in my office.
Set 13 is still with the grader.
 Statistics on the final exam: average=156/200, Median=158.
On total course score: average=80/100; median=80,82. Grades:
A, 85100; A, 7584; B+, 6074.
Homework Assignments, Second Semester
In the homework assignments, I will refer to problems in
Shankar's book by prefixing the problem number with S.
 Problem Set 1, due 11 January 2017,
Solution Set 1
 Problem Set 2, due 18 January 2017,
Solution Set 2
 Problem Set 3, due 25 January 2017,
Solution Set 3
 Problem Set 4, due 1 February 2017,
Solution Set 4
 Problem Set 5, due 8 February 2017,
Solution Set 5
 Problem Set 6, due 15 February 2017,
Solution Set 6
 Problem Set 7, due 22 February 2017,
Solution Set 7
 Midterm Examination , 1 March 2017, in class
 Problem Set 8, due 22 March 2017,
(combined with Set 9).
Solution Set 8
 Problem Set 9, due 22 March 2017,
Solution Set 9
 Problem Set 10, due 29 March 2017,
Solution Set 10
 Problem Set 11, due 5 April 2017,
Solution Set 11
 Problem Set 12, due 12 April 2017,
Solution Set 12
 Problem Set 13, due 19 April 2017,
Solution Set 13
Information on Examinations
The final exam is scheduled for Thursday, 27 April 2017, 3:005:00 pm.
The in class midterm date is Wednesday, 1 March 2017.
In grading the midterm and final exams,
points will be deducted for errors in calculation and logic.
Both exams will be closed book.
We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.
 T. S. Eliot
University Policies:
Students are expected to know and comply with
the University's policies regarding academic honesty
and use of copyrighted materials.
Cheating, plagiarism, or other violations of the Academic Honesty Guidelines
will not be tolerated and will be pursued through the University's
adjudication procedures.
“Students requesting classroom accommodations
must first register with the Disabilities Resources Program, located in
the Dean of Students Office, P202 Peabody Hall.
The Disabilities Resources Program will provide documentation to
the student, who must then deliver this documentation to the instructor
when requesting accommodations.”
Announcements, Fall 2016
 Before our first class, I strongly recommend that you watch
the video of Feynman's Messenger Lecture on Quantum Mechanics,
Cornell, 1964 linked above. We will be discussing his message
in our first class.
 Generally I would like the homework to be handed in at the
beginning of class on the due date. However, I will accept
without penalty homework handed to me in my office (not in
my mailbox!) before 5pm on the due date.
 It would be helpful
in the grading if you could
indicate on each solution the number I give to the problem,
which will be consecutive
throughout the course. For example in the first problem set my problem 3
assigns Shankar exercise 1.3.4: Please indicate it as problem 3
 I have posted the first homework Problem Set 1, 14 August 2016
 I will be out of town from 16 August 2016 until 20 August 2016,
but will be back in time for our first class Monday, 22 August 2016.
Please feel free to email me about any registration issues that
crop up during the week before classes start..
 Problem Set 2 posted 26 August 2016.
 Classes have been cancelled tomorrow (2 September)
because of tropical storm Hermine, and Monday is the
Labor Day holiday. I believe we have covered enough
material in class for you to comfortably work the problems in Problem
Set 2, so for now let's keep the due date as it is, namely
Wednesday, 7 September 2016. Please let me know by email if this will
cause undue inconvenience. If necessary I will consider
pushing back the due date.
 Problem Set 3 posted 5 September 2016.
 Solution Set 1 posted 8 September 2016.
 Problem Set 4 posted 12 September 2016.
 Solution Set 2 posted 14 September 2016.
 Problem Set 5 posted 16 September 2016.
 Solution Set 3 posted 21 September 2016.
 Problem Set 6 posted 27 September 2016.
 Solution Sets 4 and 5 posted 28 September 2016. Since everyone
handed set 5 in on time, I can post its solutions right away!
 Problem Set 7 posted 3 October 2016.
 Solution Set 6 posted 12 October 2016.
 Solution Set 7 posted 16 October 2016.
 I will be posting an exam formula sheet which will be included
in exam booklets. You may
peruse it here .
 Problem Set 8 posted 17 October 2016.
 The midterms have been graded. the range of scores was 7898,
with an average score of 88.4 and a median score of 89.
 Problem Set 9 posted 25 October 2016.
 Problem Set 10 posted 31 October 2016.
 Solution Set 8 posted 4 November 2016.
 Problem Set 11 posted 8 November 2016.
 Solution Set 9 posted 9 November 2016.
 A sudden death in my family requires me to be out of town
until Thursday. For this reason Wenesday's class (16 November) is cancelled,
to be rescheduled later. Problem Set 11 will now be due Friday (18 November)
by 5pm. Problem Set 12 will be due 30 November after Thanksgiving,
as originally planned. We will try to reschedule Wednesday's class
after I get back.
 Problem Set 12 posted 14 November 2016.
 Makeup class: Wednesday's cancelled class will be made up
on Monday, 21 November 2016 at 3pm in NPG 1220. This is the time and venue
of a cancelled EM class, which is a happy coincidence. We will meet the Monday
morning class as usual.
 Solution Set 10 posted 19 November 2016. Also please note that
online course evaluations open this Tuesday as described in the following:
 Course and teacher evaluations are conducted entirely
on line. They open Tuesday, 22 November 2016, and will continue until
until Friday, 9 December 2016, closing at midnight.
These evaluations provide very important feedback,
so it is essential that we all do our best to maximize the number of responses.
You can access the evaluation form at your leisure from the web site:
https://evaluations.ufl.edu/evals/
where you can find instructions and links to a gatorlink login page.
It is probably a good idea if you bookmark this page so you can easily find
it in the future.
 Problem Set 13 posted 29 November 2016.
 We are approaching the end of first semester. The last day I will accept
homework, including all late homework, will be the last day of class,
7 December 2016, 5pm. This means that Problem set 13, due on 7 December will
not be eligible for late submission.
 Solution Sets 11 and 12 posted 30 November 2016. Everyone
handed set 12 in on time. Bravo!
 Discussion review today at 12:30 in npb 1220!
 Solution Set 13 posted 13 December 2016.
 Statistics for final examination: Range of scores: 116172.
Average: 148.5, 74%. Median score: 145,
 Grading scale: 7079, B+; 8084, A; 85100, A.The average total
score this semester is 82.
Homework Assignments, First Semester
In the homework assignments, I will refer to problems in
Shankar's book by prefixing the problem number with S.
 Problem Set 1, due 31 August 2016,
Solution Set 1
 Problem Set 2, due 7 September 2016,
Solution Set 2
 Problem Set 3, due 14 September 2016,
Solution Set 3
 Problem Set 4, due 21 September 2016,
Solution Set 4
 Problem Set 5, due 28 September 2016,
Solution Set 5
 Problem Set 6, due 5 October 2016,
Solution Set 6
 Problem Set 7, due 12 October 2016,
Solution Set 7
 Midterm Examination, 19 October 2016
 Problem Set 8, due 26 October 2016,
Solution Set 8
 Problem Set 9, due 2 November 2016,
Solution Set 9
 Problem Set 10, due 9 November 2016,
Solution Set 10
 Problem Set 11, due 16 November 2016,
Solution Set 11
 Problem Set 12, due 30 November 2016,
Solution Set 12
 Problem Set 13, due 7 December 2016,
Solution Set 13
 Holiday Problem , for fun!
Holiday Solution
Information on Examinations
The final exam is scheduled for Friday, 16 December 2016, 7:30am9:30am, in our
regular classroom. The midterm will be given, in class, on Wednesday,
19 October 2016.
In grading the midterm and final exams,
points will be deducted for errors in calculation and logic.
Both exams will be closed book.
University Policies:
Students are expected to know and comply with
the University's policies regarding academic honesty
and use of copyrighted materials.
Cheating, plagiarism, or other violations of the Academic Honesty Guidelines
will not be tolerated and will be pursued through the University's
adjudication procedures.
“Students requesting classroom accommodations
must first register with the Disabilities Resources Program, located in
the Dean of Students Office, P202 Peabody Hall.
The Disabilities Resources Program will provide documentation to
the student, who must then deliver this documentation to the instructor
when requesting accommodations.”