PHY 274 - Fall 2009

Stony Brook University
Department of Physics and Astronomy
College of Arts and Sciences

Course Instructor: Alfred Scharff Goldhaber
goldhab max2.physics.sunysb.edu, 631 632 7975, fax 631 632 7954. Office Math 6-113.

Section: 01
Course Hours: Lecture: Tu-Th 5:20-6:40 p.m., Recitation: Tu 2:20-3:15 p.m, both in Melville Library W4530
Course credits: Four credits corresponding to four contact hours
Office Hours: To be determined, plus by appointment at class, on the phone, or on email

INTENDED AUDIENCE:

As described below, this course is designed to be fully accessible to students who have completed one year of introductory physics and the associated introductory calculus. For such students the intent is that they should feel as if the were “gliding into quantum mechanics.” As with hang gliding, first it is necessary to climb to a high place. In this case the “high place” is the properties of electromagnetic waves, well worth mastering in their own right. Students who already have more background, including Quantum Physics (our standard introductory course, PHY 308) and Advanced Quantum Physics (PHY 405) can benefit as well, because important and subtle concepts they have seen already are approached from a different perspective, reinforcing the learning.

COURSE DESCRIPTION:

Physical and mathematical foundations of quantum mechanics. Maxwell waves and their properties: Intensity, energy density, momentum density. Planck-Einstein relation between energy and frequency for light quanta. De Broglie relation between momentum and wavelength. Number density and probability density of photons. One-photon quantum mechanics, with Maxwell field as the wave function. Diffraction phenomena. Uncertainty relation between wavelength and position, hence between momentum and position. Three lecture hours and one recitation hour per week. Pre-requisites: PHY 122, or 126 and 127, or 132 and 134, or 142, MAT 132 or 142 or 127 or 171 or AMS 161. Advisory co-requisite: MAT 203, MAT 205, or equivalent.

MOTIVATION:

For more than eight decades the teaching of quantum mechanics has followed two main tracks. The first approach is at least partly historical. There is some logic to that, because if people originally found things in a certain sequence then it is at least possible for students to learn in that sequence. This is the style of "modern physics" courses, which give a broad survey of phenomena especially in microscopic physics, including many of the steps in the somewhat contorted path that led to modern quantum mechanics.

The other method is axiomatic, exemplified by Dirac's great book on the subject, a pattern followed by many more recent texts. In my opinion there is a missing piece in this traditional two-tiered approach. The intellectual jump from the broad survey to the axiomatic treatment is not easily articulated, and can be disconcerting for students as they try to negotiate the transition. The approach of the present course could be called "quasi-historical," meaning to build on a history that might have been if Einstein in 1905 had shown even greater audacity than he did in his "photoelectric effect" paper. The aim is to provide a path that is as short and direct as possible from 1905 to 1925-6, when Heisenberg and Schrödinger introduced the theory we still have today.

If short, this climb can be quite challenging, and requires an intense study of Maxwell's electromagnetic waves and their properties to provide the foundation for the ascent. The take-home message, as in Einstein's special theory of relativity, is that when one tries to fit together Maxwell's theory with other knowledge, in case of doubt one should defer to Maxwell. This may seem natural when one recognizes that Maxwell's is the first fundamental field theory in physics, still unaltered at the classical level nearly 150 years after its formulation. Thus the new course complements not only the existing one on modern physics but also other departmental offerings on aspects of electromagnetism and light.

The path, as indicated in the syllabus below, goes through Maxwell electrodynamics to one-photon quantum mechanics, and uses that as a base to develop one-electron quantum mechanics. I call this way "stronger, deeper, better" [Stronger: there is an organic connection to electrodynamics, which leads through Einstein's light quanta to photon quantum mechanics. Deeper: The two essential notions of quantized energy and photon intensity give a base for everything else. Better: These two notions allow deduction in a natural and straightforward way of most if not all the remarkable and puzzling features of quantum physics, replacing the abrupt transition from a modern physics course to a formal course.]

I believe this approach could help overcome what seems to me a deficiency in current physics training, that students are exposed to classical mechanics and classical electrodynamics twice during their undergraduate years, but a systematic approach to quantum physics just comes along at the end. My idea is that this should be a first-term sophomore course, simultaneous with and complementing the Modern Physics course, allowing students to enter PHY 308, Quantum Physics, in the spring of sophomore year. This would be a one-year speed-up compared to the current pattern here, and would put our program on the same pace (with respect to quantum physics) as many other colleges. Colleagues at a number of other institutions have introduced quantum mechanics through light rather than through massive particles like electrons, but I'm unaware of any textbook which does this. While intended to be accessible to sophomores, the course also can be useful and appropriate for juniors still before taking 308, and even seniors who would like a chance to get another perspective on the path to quantum mechanics. As mentioned above, another way to view the goal of this course is “gliding into quantum mechanics.” As in hang-gliding, you must make a steep climb before you can start the glide. The climb is through understanding the Maxwell equations and their free solutions, the first-discovered fundamental waves in physics. When we begin the glide, we recognize these solutions as quantum-mechanical waves describing the behavior of photons, or particles of light.

COURSE PRE-REQUISITES:

Introductory classical mechanics and electromagnetism. Introductory differential and integral calculus. Advisory co-requisite -- Multivariable calculus. Because the Maxwell equations involve three space dimensions, and time, for the vector electric and magnetic fields, they give a wonderful laboratory for working with multivariable calculus. Having that course beforehand or concurrently would give extra and possibly complementary perspective on these properties, but all that is needed will be worked out fully in PHY 274.

COURSE OBJECTIVES:

Complements PHY 251 Modern Physics and prepares a foundation for PHY 308 Quantum Physics, by arriving first at one photon-quantum mechanics through the principles indicated (thought not fully worked out) in Einstein’s 1905 paper on the photo-electric effect, and then deriving the Schrödinger equation.

COURSE REQUIREMENTS:

Attendance and Make Up Policy
One-half point homework-problem credit per week for attendance. A quarter point if late to class. Late homework may be graded down, depending on circumstances. Both for homework and for attendance excused lateness or absence will not count against the student.

Exams
None.

Grading
Ten homework sets during the term, with a possible 5 points for each set (one per problem). Up to 16 points for attendance. Up to 20 points for homework solution presentations or special presentations in class (which may be accompanied by short papers that can be distributed to the class). Up to 14 points for valuable comments or questions in class, or on Blackboard.
Letter grades: >95=A, >90 =A-, >85=B+, >80=B, >75=B-, >70=C+, >65=C, >60=C-.
Actual letter grades will not be lower than these guidelines, but might be higher.

MEETING SCHEDULE

No exams. Topics indicated by week:

CLASS PROTOCOL

Cell phone and electronic device statement: Everyone, including the instructor, is permitted to bring devices to class, but they must be in quiet mode. Under normal circumstances, incoming calls should not be answered during class. Students are free to make audio or video recordings of the class, and are permitted to post these recordings on the blackboard site. It has been announced that our classroom will be equipped for videorecording. Once this has been established, I plan to make the video-record available through Blackboard.

CLASS RESOURCES

Library resources: Some texts will be put on reserve in the Math-Physics library. Blackboard will be used extensively, and students are strongly encouraged to post comments or questions relating to the class, anonymously if they wish. Of course, to get credit for an apt comment or question, one must not post anonymously!

Two recommended textbooks (#1 and #2), and one reference book (#3) from the Schaum Outline Series:

DISABILITY SUPPORT SERVICES (DSS) STATEMENT

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.

Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities ]

ACADEMIC INTEGRITY STATEMENT

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/

CRITICAL INCIDENT MANAGEMENT

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.