Instructor: Doug Pickrell
Office: Mathematics 703
Office Phone: 621-4767
Email: pickrell@math.arizona.edu
Office Hours: TuTh 12:30-1:30
Text: Leon Takhtajan, Lectures on Quantum Mechanics for Mathematics Students. Other recommended books: Mathematical Methods of Classical Mechanics by V.I. Arnold, Quantum Mechanics for Mathematicians, Brian Hall, Lectures on Quantum Mechanics for Mathematics Students, L.D. Faddeev and O.A. Yakubovskii
About the course: This will be a basic course, intended for math students who do not have much of a background in physics, and for physics students who would like to understand the mathematical framework of classical and quantum physics in a more rigorous way. I will be using the book Quantum Mechanics for Mathematicians by Takhtajan. This book is quite sophisticated from a mathematical point of view, so I will fill in a fair amount of the background which the author assumes as we go along. The course will be divided into three parts, and the parts will be somewhat independent. The first part of the course (chapter 1 of the book) will be an introduction to classical mechanics (and a tiny bit of statistical mechanics), especially the modern formulation of Hamiltonian mechanics in terms of symplectic geometry. This involves some familiarity with tensors, especially differential forms. I am hoping that physics students will have seen this before, in some form, so that the level of sophistication in the book is not too much of a shock. The second part will introduce quantum mechanics. From a mathematical point of view, this involves the spectral theorem (for unbounded operators), which we will do from scratch. We will repeat a lot of standard things from physics, such as solving for the energy levels of the hydrogen atom. We will probably do some scattering theory, and perhaps some quantum information theory, or entanglement (which is not in the book, and I will have to think about this). In the last part of the course I would like to introduce Feynman path integrals (from a mathematical point of view, Brownian motion or Wiener measure). There is a lot of hard mathematics involved here, so I do not know how interesting this will be from a physicist's point of view.
Expectations: I will assign homework about every two weeks, and send out some solutions. I hope to recruit participants in the class to present some of the applications of the material in the context of the course. There will not be any exams.
Grades: To earn an A in the course, a graduate student will be expected to demonstrate understanding of the material at a graduate level. This can be done in multiple ways: by doing the homework, by doing a project, by giving a presentation (to the class, or to me),...
Attendance: Students are expected to attend every scheduled class. • The UA’s policy concerning Class Attendance, Participation, and Administrative Drops is available at: http://catalog.arizona.edu/policy/class-attendance-participation-and-administrative-drop. • The UA’s policy regarding absences for any sincerely held religious belief, observance or practice will be accommodated where reasonable. See: http://policy.arizona.edu/human-resources/religious-accommodation-policy. • Absences pre-approved by the UA Dean of Students (or Dean Designee) will be honored. See: https://deanofstudents.arizona.edu/absences.
Classroom Behavior: To foster a positive learning environment, students and instructors have a shared responsibility. We want a safe, welcoming, and inclusive environment where all of us feel comfortable with each other and where we can challenge ourselves to succeed. To that end, our focus is on the tasks at hand and not on extraneous activities (texting, chatting, reading a newspaper, making phone calls, web surfing).
Communication: It is the student’s responsibility to keep informed of any announcements, syllabus adjustments or policy changes made during scheduled classes, by email.
Students with disabilities: Our goal in this classroom is that learning experiences be as accessible as possible. If you anticipate or experience physical or academic barriers based on disability, please let me know immediately so that we can discuss options. You are also welcome to contact the Disability Resource Center (520-621-3268) to establish reasonable accommodations. For additional information on the Disability Resource Center and reasonable accommodations, please visit http://drc.arizona.edu. If you have reasonable accommodations, please plan to meet with me by appointment or during office hours to discuss accommodations and how my course requirements and activities may impact your ability to fully participate. Please be aware that the accessible table and chairs in this room should remain available for students who find that standard classroom seating is not usable.
Students withdrawing from the course: Must be made in accordance with University policy http://catalog.arizona.edu/policy/grades-and-grading-system#Withdrawal.
Incompletes: Must be made in accordance with University policies, which are available at http://catalog.arizona.edu/policy/grades-and-grading-system#incomplete
University Policies: • The UA Threatening Behavior by Students Policy prohibits threats of physical harm to any member of the University community, including to oneself. See http://policy.arizona.edu/education-and-student-affairs/threatening-behavior-students. • Students are encouraged to share intellectual views and discuss freely the principles and applications of course materials. However, graded work/exercises must be the product of independent effort unless otherwise instructed. Students are expected to adhere to the UA Code of Academic Integrity as described in the UA General Catalog. See: http://deanofstudents.arizona.edu/academic-integrity/students/academic-integrity. • The University is committed to creating and maintaining an environment free of discrimination; see http://policy.arizona.edu/human-resources/nondiscrimination-and-anti-harassment-policy
Note: Information contained in the course syllabus, other than the grade and absence policy, may be subject to change with advance notice, as deemed appropriate by the instructor.