Contact Information
Goals and Requirements
Method of Evaluation
Course Content
Important Dates
Course Schedule
Students are required to be thoroughly familiar with the fundamentals of quantum mechanics, both with the wavefunction approach and with the Dirac bra-ket formalism. Thorough familiarity with quantum mechanics at the undergraduate level is expected. This includes, but is not limited to an understanding of one and three-dimensional versions of problems such as that of a particle in a box, the simple harmonic oscillator and the hydrogen atom. Students should understand state vectors and operators and their matrix representations. They should be thoroughly familiar with the concept of representing state vectors in position and momentum space and indeed as expansions in any basis. Similarly, they should be familiar with the idea of representing operators in any basis.
It is expected that students know about unitary transformations and have used all unitary transformation operators such as the spatial translation operator, the time evolution operator and operators for rotation. An understanding of the time evolution of quantum systems is critically necessary to the progress they are expected to make in this course. Students must be able to use all the concepts mentioned in both the Schrodinger and Heisenberg pictures. Students are expected to be familiar with propagators, path integrals, gauge transformations, Bell's inequality and the Aharanov-Bohm effect, all of which are topics that illustrate the fundamental physics in quantum mechanics.
Finally, students are expected to be familiar with the theory of angular momentum. They must know how to deal with systems of arbitrary spin and with systems where more than one angular momentum is present. Knowledge of the addition of angular momenta is critical in most physical applications of quantum mechanics. Students should know when density operators and mixed ensembles are needed in physical problems and also how they should be employed. Their understanding of angular momentum must include knowledge of orbital angular momenta and tensor operators.
A secondary but nevertheless critically important goal of this course arises from the fact that it is a core graduate course. Therefore one of the goals of this course is to prepare students for the Quantum Mechanics Section of the Admission to Candidacy Examination. This is why there are so many homework problems. Students who do well in this course can reasonably expect to do well in the Quantum Mechanics Section of the Admission to Candidacy Examination.
Homework = 35%, In Class Exams = 30%, Final Exam = 35%.
Each in-class exam has equal weightage, i.e., each exam counts for 10%
of your final grade.
You will need at least 90% for an A, 85% for a B+, 75% for a B,
70% for a C+ and 60% for a C.
Homework:
You must read roughly 10 pages or 1 section of Sakurai as preparation
for each lecture. Ideally, students should read material prior to a
lecture, pay close attention during the lecture and ask questions if
they are still unclear about anything. Do not hesitate to ask questions
- even when many students in class are puzzled only one may be brave
enough to ask! Don't think you are the only one who is confused and / or
that asking a question reflects poorly on you in any way. Remember,
grades are earned via homeworks and exams, questions are merely to
understand the material better.
Two or more homework problems will be assigned every day and they will
be due in one week.
Late homework receives only 50% points if submitted within one week of
due date. After that, late homework should not be submitted - there will
be no credit given.
Exams:
If you miss an exam you must
(A) Have a valid medical reason and a doctor's note.
(B) Your grade will then be just the average of your other exam scores,
i.e., there will be no special tests for students who miss their
exams. If you miss an exam without a valid reason, you get zero for the
exam.
Attendance: Mandatory!
As mentioned above, the emphasis in this course is on formal techniques and different approaches to quantum mechanics are explained.
We begin this course with a discussion of symmetry operations in quantum mechanics. In particular, we discuss both continuous symmetries such as rotational symmetry as well as discrete symmetries such as parity and time reversal. In this course students will learn how to deal with identical particles and the constraints that they impose. This topic is illustrated by two-electron systems such as the helium atom.
The main thrust of this course, the second half of the graduate quantum mechanics course, is in learning how to deal with applications of quantum mechanics. A considerable amount of time goes into dealing with atomic physics and other applications well suited to approximation methods such as time-dependent and time-independent perturbation theory. Another important topic covered in this context is the interaction of atoms with electromagnetic radiation.
The course concludes with an introduction to scattering theory. After an introduction to the subject, students will learn about the Born approximation and the optical theorem. Spherical waves are introduced along with the method of partial waves which is a powerful way to deal with many scattering problems. Modifications dealing with identical particles and symmetry considerations are then considered. Finally, we also study resonance scattering and inelastic scattering.
Essentially all of the material is contained in chapters 4-7 of the text by Sakurai. The introductory material on scattering theory is better explained in Griffiths; Sakurai should be used for the advanced aspects.