Courses in LSA Physics

Physics (PHYSICS)

PHYSICS 401. Intermediate Mechanics
PHYSICS 351 or graduate standing.
(Prerequisites enforced at registration.)
PHYSICS 340 or 360 and one of MATH 216, 256, 286, or 316.
(4).
(BS).
(QR/1).
May not be repeated for credit.
Newtonian and Lagrangian mechanics: Kinematics and dynamics in one, two, and three dimensions, vector analysis; motion under gravity, planetary motion; free and forced, damped and undamped harmonic oscillators; the conservation laws of mechanics; inertial and accelerated frames of reference, fictitious forces; rigid body mechanics; coupled oscillators.

PHYSICS 402. Optics
PHYSICS 340 or 360, and one of: MATH 216, 256, 286, 296 or 316: or graduate standing.
(Prerequisites enforced at registration.)
(3).
(BS).
May not be repeated for credit.
A student can receive credit for only one of EECS 334 or PHYSICS 402.
Topics studied cover the phenomena of physical optics, reflection, refraction, interference, diffraction, and polarization interpreted in terms of the wave theory of light. Selected topics in contemporary optics, such as adaptive optics, fiber optics, human vision, etc. also will be covered.

PHYSICS 405. Intermediate Electricity and Magnetism
PHYSICS 351 or graduate standing.
(Prerequisites enforced at registration.)
PHYSICS 340 or 360, and one of: MATH 216, 256, 286, or 316.
(4).
(BS).
May not be repeated for credit.
This course provides a rigorous introduction to electricity and magnetism, suitable for junior year physics majors or engineering students. Subjects include static electric fields in vacuum, in matter and in vacuum and matter. Also includes timedependent phenomena, electromagnetic induction and Maxwell's equations.

PHYSICS 406. Statistical and Thermal Physics
(PHYSICS 340 or 360) and PHYSICS 351, or graduate standing.
(Prerequisites enforced at registration.)
(4).
(BS).
May not be repeated for credit.
The course in an introduction to thermal processes, including the classical laws of thermodynamics and their statistical foundations. Topics discussed are: basic probability concepts, statistical description of systems of particles, thermal interaction, microscopic basis of macroscopic concepts such as temperature and entropy, laws of thermodynamics, elementary kinetic theory of transport processes.

PHYSICS 411. Introduction to Computational Physics
PHYSICS 401 and [MATH 216 or 256 or 286 or 296 or 316]. Some familiarity with a computer language.
(3).
(BS).
May not be repeated for credit.
Introduction to techniques of computational physics with applications in optics, atomic, solidstate, nuclear and particle physics.

PHYSICS 413 / CMPLXSYS 541. Introduction to Nonlinear Dynamics and the Physics of Complexity
PHYSICS 401 or Graduate Standing.
(Prerequisites enforced at registration.)
An intermediate mechanics course (such as PHYSICS 401) and/or a course in introductory differential equations.
(3).
(BS).
May not be repeated for credit.
F.
An introduction to nonlinear science with an elementary treatment from the point of view of the physics of chaos and fractal growth.

PHYSICS 417 / BIOPHYS 417 / CHEM 417. Dynamical Processes in Biophysics
MATH 216 or 256 or 286 or 296 or 316; and BIOPHYS 370 or PHYSICS 340 or PHYSICS 360 or PHYSICS 370 or CHEM 463 or CHEM 370.
(Prerequisites enforced at registration.)
(3).
(BS).
May not be repeated for credit.
The physical basis of diffusive processes in biology and biochemistry, and optical spectroscopic means for measuring its rates. Topics include: membrane electrical potentials, nerve impulses, synaptic transmission, the physics of chemoreception by cells, motion and reaction kinetics of membrane components, optical microscopy, visible and UV light absorption, fluorescence and phosphorescence, quasielastic light scattering, mathematics of random fluctuations, and chaotic processes in biology.

PHYSICS 420. Physics for Educators
School of Education concentrators.
(3).
May not be repeated for credit.
No credit granted to those who have completed or are enrolled in PHYSICS 106.
W.
This course is a survey course for students preparing to teach at the elementary classroom level. The goal of the course is to provide a good and practical appreciation of the basic laws that govern our universe. In addition to homework questions there will be a variety of handson activities designed to demonstrate the rules of physics in action which might be adapted for use in elementary classrooms.

PHYSICS 433 / BIOPHYS 433. Biocomplexity
BIOPHYS 417 or CHEM 417 or PHYSICS 417, or PHYSICS 406; or graduate standing.
(Prerequisites enforced at registration.)
(3).
(BS).
May not be repeated for credit.
Rackham credit requires additional work.
This course on biocomplexity explores concepts of nonlinear dynamics and the interplay between chaos and order in biological systems.

PHYSICS 435. Gravitational Physics
PHYSICS 390 and 401; or graduate standing.
(Prerequisites enforced at registration.)
(3).
(BS).
May not be repeated for credit.
F.

PHYSICS 438. Electromagnetic Radiation
PHYSICS 405.
(Prerequisites enforced at registration.)
(3).
(BS).
May not be repeated for credit.

PHYSICS 441. Advanced Laboratory I
PHYSICS 390 and any 400level Physics course.
(Prerequisites enforced at registration.)
(3).
(BS).
May not be repeated for credit.
F.

PHYSICS 442. Advanced Laboratory II
PHYSICS 441.
(Prerequisites enforced at registration.)
(3).
(BS).
May not be repeated for credit.
W.
This is the second semester advanced laboratory course. A wide selection of individual experiments are offered. Students must select 5 experiments from several different areas of physics in consultation with the lab instructor.

PHYSICS 450 / BIOPHYS 450. Laboratory Techniques in Biophysics
BIOPHYS 370 or CHEM 370 or PHYSICS 370; or PHYSICS 390; or CHEM 452 or BIOLCHEM 452; or graduate standing.
(Prerequisites enforced at registration.)
(3).
(BS).
May not be repeated for credit.
Rackham credit requires additional work.
This laboratory course teaches essential laboratory skills in biophysics through handson experiments, computational work, and a supporting lecture.

PHYSICS 452. Methods of Theoretical Physics II
PHYSICS 351.
(3).
(BS).
May not be repeated for credit.
This is an advanced course for undergraduate physics majors who need necessary preparation for graduate school. This course is also recommended to the firstyear graduate student. The course will cover 1) group theory; 2) Hilbert Spaces; 3) special functions and properties; 4) boundary value problems and Green's function technique; and 5) calculus of variations.

PHYSICS 453. Quantum Mechanics
PHYSICS 351 and PHYSICS 390; or graduate standing.
(Prerequisites enforced at registration.)
PHYSICS 401 and PHYSICS 405.
(4).
(BS).
May not be repeated for credit.
This course provides an introduction to quantum mechanics at the advanced undergraduate level. The underlying principles of quantum mechanics are discussed, with an emphasis placed on solutions of both the timedependent and timeindependent Schrodinger equations. Topics covered include quantization of angular momentum and the theory of the hydrogen atom.

PHYSICS 457. Particle Physics and Cosmology
PHYSICS 453; or graduate standing.
(Prerequisites enforced at registration.)
(3).
(BS).
May not be repeated for credit.
W.
This course is an introduction to particle physics and cosmology. It covers the following: quarks and leptons and their interactions; conservation laws and symmetries; gauge theories and the standard model of particle physics; the expanding universe; nucleosynthesis; dark matter; and dark energy in the universe and large scale structure. Students are assumed to have basic knowledge of quantum mechanics and special relativity.

PHYSICS 460. Quantum Mechanics II
PHYSICS 453; or graduate standing.
(Prerequisites enforced at registration.)
(3).
(BS).
May not be repeated for credit.
W.

PHYSICS 463. Introduction to Solid State Physics
PHYSICS 453; or graduate standing.
(Prerequisites enforced at registration.)
(3).
(BS).
May not be repeated for credit.
W.

PHYSICS 489. Physics of Music
Permission of instructor.
(3).
(QR/1).
May not be repeated for credit.

PHYSICS 501. FirstYear MiniColloquium
PHYSICS,First Year Graduate Status.
(1).
(BS).
May be elected twice for credit.
This course has a grading basis of "S" or "U".
Course designed specifically for 1st year Physics graduate students. Course objective is to learn about research opportunities within the Physics graduate studies program.

PHYSICS 505. Electricity and Magnetism I
Graduate Standing.
(3).
(BS).
May not be repeated for credit.

PHYSICS 506. Electricity and Magnetism II
Graduate Standing.
(3).
(BS).
May not be repeated for credit.

PHYSICS 507. Theoretical Mechanics I
Graduate Standing.
(3).
(BS).
May not be repeated for credit.

PHYSICS 508 / CMPLXSYS 535. Theory of Social and Technological Networks
Calculus and linear algebra; some computer programming experience recommended.
(3).
(BS).
May not be repeated for credit.
Introduce and develop the mathematical theory of networks, particularly social and technological networks; applications to important networkdriven phenomena in epidemiology of human infections and computer viruses, cascading failure in grids, network resilience and opinion formation. Topics covered: experimental studies of social networks, WWW, internet, information, and biological networks.

PHYSICS 510. Statistical Physics I
PHYSICS 406 and Graduate standing.
(3).
(BS).
May not be repeated for credit.

PHYSICS 511. Advanced Quantum Mechanics I
Graduate Standing.
(3).
(BS).
May not be repeated for credit.
This is the first course in a twoterm sequence on the quantum theory and its applications to nonrelativistic atomic, molecular, nuclear and solid state systems; time independent and time dependent perturbation theory; angular momentum, scattering theory; interaction of photons with nonrelativistic systems; the Dirac equation.

PHYSICS 512. Advanced Quantum Mechanics II
Graduate standing. Permission of instructor required.
(3).
(BS).
May not be repeated for credit.
This is the second course in a twoterm sequence on the quantum theory and its applications to nonrelativistic atomic, molecular, nuclear and solid state systems; time independent and time dependent perturbation theory; angular momentum, scattering theory; interaction of photons with nonrelativistic systems; the Dirac equation.

PHYSICS 513. Quantum Field Theory I
Graduate standing.
(3).
(BS).
May not be repeated for credit.
Introduction to the methods of relativistic quantum field theory with applications relevant to high energy physics. Topics include: classical field theory, quantization, the path integral, Feynman diagrams, and calculation of treelevel scattering cross sections for simple processes in scalar theories and Quantum Electrodynamics.

PHYSICS 514. Computational Physics
Graduate standing or permission of instructor.
(3).
May not be repeated for credit.
Techniques of computational physics with applications to classical and quantum systems.

PHYSICS 515. Supervised Research
Consent of instructor required.
Graduate standing and permission of instructor.
(4  6).
(INDEPENDENT).
May be repeated for credit.
This course has a grading basis of "S" or "U".

PHYSICS 516. Supervised Research
Consent of instructor required.
Graduate standing and permission of instructor.
(4  6).
(INDEPENDENT).
May not be repeated for credit.
This course has a grading basis of "S" or "U".

PHYSICS 517 / APPPHYS 517 / BIOPHYS 517. Nanobiology Certificate Seminar
(2).
May not be repeated for credit.
This course has a grading basis of "S" or "U".
In this seminar course students will see presentations from researchers in a number of fields important to nanobiology. Advanced students will be able to present material from their own research experiences.

PHYSICS 520. Condensed Matter Physics
PHYSICS 510, 511 or equivalent, and Graduate standing.
(3).
(BS).
May not be repeated for credit.

PHYSICS 521. Elementary Particle Physics I
PHYSICS 512 and Graduate standing.
(3).
(BS).
May not be repeated for credit.

PHYSICS 522. Atomic Physics and Quantum Mechanics
Graduate standing.
(3).
(BS).
May not be repeated for credit.

PHYSICS 523. Quantum Field Theory II
PHYSICS 513 and Graduate standing.
(3).
(BS).
May not be repeated for credit.
Advanced course in relativistic quantum field theory with emphasis on renormalization. Infrared and ultraviolet divergence's are discussed in detail and interpreted using modern effective field theory. Among the topics explored are unitarity of abelian and nonabelian gauge theories, spontaneous symmetry breaking, and renormalization group.

PHYSICS 525. Cosmology I  The Early Universe
Graduate standing.
(3).
(BS).
May not be repeated for credit.
From the big bang to the epoch of cosmic microwave background. Physics of the expanding universe, Einstein and Boltzmann equations, inflation, big band nucleosynthesis, recombination and early universe probes of inhomogeneities up to the CMB epoch. Special topics.

PHYSICS 526. Cosmology II  The Late Universe
Graduate standing.
(3).
(BS).
May not be repeated for credit.
From the cosmic microwave background until today. Broad overview of astrophysics, stars and galaxies, followed by basics of the hot big bang model, nucleosynthesis, cosmic microwave background, large scale structure, and gravitational lensing. Cosmological probes of dark energy and dark matter.

PHYSICS 535. General Relativity
Graduate standing.
(Prerequisites enforced at registration.)
PHYSICS 390 and 401.
(3).
May not be repeated for credit.
This course is a thorough introduction to the theory of general relativity, covering both its mathematical underpinnings and its implications for gravitational physics. Topics include: tensor analysis, curved manifolds and differential geometry, the Einstein field equations, gravitational radiation, black holes, experimental tests of general relativity and standard cosmological models.

PHYSICS 540 / APPPHYS 601. Advanced Condensed Matter
Graduate standing.
(3).
(BS).
May not be repeated for credit.

PHYSICS 541. Elementary Particle Physics II
PHYSICS 521 and Graduate standing.
(3).
(BS).
May not be repeated for credit.

PHYSICS 542 / EECS 638. Quantum Optics
PHYSICS,Quantum mechanics, electrodynamic and atomic physics.
(3).
(BS).
May not be repeated for credit.

PHYSICS 608 / BIOPHYS 608 / MCDB 608. Biophysical Principles of Microscopy
PHYSICS,Knowledge of complex exponential notation, and graduate standing. Physics 405 or permission of instructor.
(3).
May not be repeated for credit.

PHYSICS 611 / APPPHYS 611 / EECS 634. Nonlinear Optics
EECS 537 or 538 or 530. Graduate standing.
(3).
(BS).
May not be repeated for credit.
Formalism of wave propagation in nonlinear media; susceptibility tensor; second harmonic generation and threewave mixing; phase matching; third order nonlinearities and fourwave mixing processes; stimulated Raman and Brillouin scattering. Special topics: nonlinear optics in fibers, including solitons and selfphase modulation.

PHYSICS 613. Topics in Advanced Quantum Theory
PHYSICS 512 and Graduate standing.
(3).
May not be repeated for credit.

PHYSICS 619 / APPPHYS 619. Advanced Solid State Physics
Graduate standing.
(3).
May not be repeated for credit.

PHYSICS 620 / APPPHYS 620. Advanced Condensed Matter Physics
Graduate standing and permission of instructor.
(3).
May be repeated for a maximum of 9 credits.
This course has a grading basis of "S" or "U".
An advanced course in condensed matter physics. It provides an introduction to basic subjects not covered in linear response and group theory as well as a presentation of topics of current interest such as the quantum Hall effect and superconductivity.

PHYSICS 621. Quantum Theory of Fields
Graduate standing and permission of instructor.
(3).
May be repeated for a maximum of 6 credits.

PHYSICS 625. Theory of Elementary Particles
Graduate standing and permission of instructor.
(3).
May not be repeated for credit.

PHYSICS 628. Experimental Collider Physics
Graduate standing and permission of instructor.
(3).
May not be repeated for credit.
The course will cover techniques and physics of modern hadron collider experiment. Specifically, it will be organized in the following six main areas: collider detector, quantum chromodynamics, electroweak physics, to quark production and decays, B physics, and physics beyond the standard model.

PHYSICS 630. Biological Physics
Graduate standing or permission of instructor.
(3).
May not be repeated for credit.
An introduction to biological physics at the cellular and supracellular scales, with an emphasis on understanding how robust biological function emerges from the interactions of systems of molecules, genes, and cells. Topics will be drawn from research literature of the past 20 years including signal transduction and cellular information processing, the effects of noise in living cells, the active mechanics of the cytoskeleton, and pattern formation and morphogenesis in animal development. We will pay particular attention to the process of modelbuilding and the role that quantitative, physical models can play in shaping our understanding of biological systems. Physical and mathematical background developed as needed.

PHYSICS 644 / APPPHYS 644. Advanced Atomic Physics
Graduate standing.
(3).
May not be repeated for credit.

PHYSICS 646. String Theory
The ideal preparation for this course is general relativity and introductory quantam field theory; however, the course can also be taken by motivated students with strong background in quantum theory.
(3).
May not be repeated for credit.
This course has a grading basis of "S" or "U".
String Theory is the only quantum mechanically consistent formulation of gravity we know. This course is an introduction to the quantum theory of relativistic strings and its modern applications. The focus will be on perturbative techniques based on conformal field theory in two dimensions. Important examples will be Dbranes, toroidal compactification and orbifolds. The course provides the foundation needed for applications of string theory to strongly gravitating systems such as black holes and cosmology as well as to particle physics.

PHYSICS 650 / APPPHYS 550 / EECS 538. Optical Waves in Crystals
EECS 434 and Graduate standing.
(3).
(BS).
May not be repeated for credit.

PHYSICS 651 / APPPHYS 551 / EECS 539. Lasers
EECS 537 or 538 and Graduate standing.
(3).
(BS).
May not be repeated for credit.

PHYSICS 667. Advanced Astrophysics
Graduate standing and permission of instructor.
(3).
May not be repeated for credit.

PHYSICS 690. Special Topics in Physics
Graduate standing.
(3).
May be elected three times for credit.
This course has a grading basis of "S" or "U".
This course will be offered sporadically by the Physics Dept. The special topics designation is necessary because we frequently have visiting scholars and/or visiting professors who wish to teach graduate level courses that currently do no exist. The content will vary from term to term, which is why the course may be repeated.

PHYSICS 715. Special Problems
Consent of instructor required.
Graduate standing and permission of instructor.
(1  6).
(INDEPENDENT).
May not be repeated for credit.

PHYSICS 990. Dissertation/Precandidate
Election for dissertation work by doctoral student not yet admitted as a Candidate. Graduate standing.
(1  8; 1  4 in the halfterm).
(INDEPENDENT).
May be repeated for credit.
This course has a grading basis of "S" or "U".

PHYSICS 993. Graduate Student Instructor Training Program
Must have Teaching Assistant award. Graduate standing and permission of instructor.
(1).
May not be repeated for credit.
This course has a grading basis of "S" or "U".

PHYSICS 995. Dissertation/Candidate
Graduate School authorization for admission as a doctoral Candidate.
(Prerequisites enforced at registration.)
(8; 4 in the halfterm).
(INDEPENDENT).
May be repeated for credit.
This course has a grading basis of "S" or "U".
