### Physics

**School/College**: College of Letters and Science

**Degrees Conferred:**

- M.S. in Physics
- Ph.D. in Physics

#### Contents

#### Overview

The Physics Department is a young department with exceptional strength in several areas. We invite applications from able students interested in experimental and theoretical surface physics and condensed matter physics; in experimental modern optics; in quantum gravity, quantum field theory, cosmology, and relativistic astrophysics; and in physics teaching at a high-school or college level. The primary goal of our graduate education is the training of creative research scientists.

Our research in gravitational physics is in several areas: In gravitational-wave astronomy, we play a leading role in the development for LIGO of templates to extract signals of gravitational-waves from the coalescence of binary neutron stars and from the stochastic background. In early cosmology, recent work includes renormalization methods to investigate inflationary models. In the quantum arena, work involves black-hole evaporation and information loss, and quantization of microscopic topological structures. In relativistic astrophysics we have established limits on the spin and mass of rotating neutron stars. Work in nuclear physics and particle physics includes a study incorporating gluon exchange and quark confining interactions into relativistic bound-state equations, and a study of production mechanisms for the Higgs boson and related intermediate mass bosons.

Research in theoretical physics also includes work in graph theory, fiber bundles, homotopy classes of diffeomorphisms, the quantum theory of measurement and black-hole entropy and information loss. Theoretical work in nonlinear dynamics and chaos concerns maps approximating dynamical systems.

Research in surface physics includes experimental work in electron microscopy, electron holography, electron diffraction, scanning tunneling microscopy and spectroscopy, atomic force microscopy, infrared spectroscopy, synchrotron radiation, and molecular beam epitaxy.

Theoretical work in surface physics focuses on the structure and dynamics of surfaces and interfaces. The theory groups have developed quantum mechanical multiple scattering theories for electron and positron diffraction, photoelectron diffraction, high-resolution electron-energy-loss spectroscopy, x-ray diffraction, and electron holography.

Experimental work in condensed matter physics is also being done in the areas of low-temperature physics, unconventional superconductivity (including high Tc), heavy fermions, materials synthesis and floating zone single crystal growth, oxides, magnetism, ultrasonics, and neutron diffraction. Theoretical work in condensed matter physics also includes research in quantum transport phenomena and electromigration in mesoscopic systems, and superconductivity.

Experimental work in modern optics is being done with ultrafast lasers to study the dynamics of physical, chemical, and biological systems on the molecular and cellular level.

##### Graduate Minor in Physics

A doctoral student in another department wishing to minor in Physics must choose a minor professor from among the Physics Graduate Faculty. The student and the minor professor plan a program of study consisting of 9 to 12 graduate credits in Physics and complete a Graduate Minor Program Plan for the Physics Department files.

#### Graduate Faculty

- Distinguished Professors
- Ourmazd, Abbas, D.Phil., Oxford University, England
- Saldin, Dilano, D.Phil., Oxford University, England
- Weinert, Michael, Ph.D., Northwestern University

- Professors
- Agterberg, Daniel, Ph.D., University of Toronto, Canada
- Brady, Patrick, Ph.D., University of Alberta, Canada
- Creighton, Jolien, Ph.D., University of Waterloo, Canada
- Gajdardziska-Josifovska, Marija, Ph.D., Arizona State University
- Guptasarma, Prasenjit, Ph.D., University of Bombay, India
- Hirschmugl, Carol J., Ph.D., Yale University
- Li, Lian, Ph.D., Arizona State University
- Lyman, Paul F., Ph.D., University of Pennsylvania
- Raicu, Valerica, Ph.D., University of Bucharest, Romania, Chair
- Sarma, Bimal, Ph.D., Northwestern University
- Schmidt, Marius, Dr. rer. nat., Technical University of Munich, Germany

- Associate Professors
- Anchordoqui, Luis, Ph.D., Universidad Nacional La Plata, Argentina
- Patch, Sarah, Ph.D., University of California-Berkeley
- Siemens, Xavier, Ph.D., Tufts University
- Wiseman, Alan, Ph.D., Washington University
- Kaplan, David, Ph.D., California Institute of Technology
- Erb, Dawn, Ph.D., California Institute of Technology
- Schwander, Ph.D., ETH, Zurich, Switzerland

- Assistant Professors
- Chang, Phil, Ph.D., University of California, Santa Barbara

#### Master of Science in Physics

##### Admission

An applicant must meet Graduate School requirements plus these departmental requirements to be considered for admission to the program:

- Letters of Recommendation. Three letters of recommendation are required from persons familiar with the applicant's academic work.
- Graduate Record Examinations. Both the General Test and the Subject Test in Physics are strongly encouraged (but not required).
- Undergraduate major in physics or related fields. Applicants may be admitted with specific program-defined course deficiencies provided that the deficiencies amount to no more than two courses.

The student is expected to satisfy deficiency requirements within three enrolled semesters. The deficiencies are monitored by the Graduate School and the individual graduate program unit. No course credits earned in making up deficiencies may be counted as program credits required for the degree.

##### Major Professor as Advisor

The student must have a major professor to advise and supervise the student's studies as specified in Graduate School regulations. The newly admitted student is assigned to a temporary advisor.

Students in the master's program who are planning to terminate their physics studies with a master's degree should plan and prepare a program of study with the Department Master's Program Advisor.

##### Option 1: Thesis Option

###### Credits and Courses

Minimum degree requirement is 30 graduate credits, 18 of which must normally be in physics and 12 of which may be in related fields. Of the 18 credits earned in the Department, at least 6 must be in physics courses numbered above 700, with the remainder in courses at least above 500; research, seminar, and independent study credits do not satisfy the 700 requirement. Six credits are earned through the thesis.

###### Thesis

The student must write an acceptable thesis.

###### Comprehensive Examination

The student must pass a comprehensive oral examination, in part a defense of the thesis.

###### Time Limit

The student must complete all degree requirements within five years of initial enrollment.

##### Option 2: Non-thesis Option

###### Credits and Courses

Minimum degree requirement is 30 graduate credits, 18 of which must normally be in physics and 12 of which may be in related fields. Of the 18 credits earned in the Department, at least 6 must be in physics courses numbered above 700, with the remainder in courses at least above 500; research, seminar, and independent study credits do not satisfy the 700 requirement.

###### Thesis

Not required.

###### Comprehensive Examination

The student must pass a comprehensive written or oral examination. The non-thesis master's Oral Examination should evaluate the student's achievements in graduate courses and fulfillment of the goals of the student's program of study. In particular, students should be familiar with the materials in the "core" courses (Physics 515, 531, 532, 711 and 720).

###### Time Limit

The student must complete all degree requirements within five years of initial enrollment.

##### Doctor of Philosophy in Physics

##### Admission

Applicant must meet Graduate School requirements plus departmental requirements as given for admission to the master's program. A master's degree is not a prerequisite for this Ph.D. program.

##### Reapplication

A student who receives the master's degree must formally reapply for admission to the Graduate School before continuing studies toward the Ph.D.

##### Course of Study

Minimum degree requirement is 54 graduate credits beyond the bachelor's degree, at least 27 of which must be earned in residence at UWM. The student plans an individual program of studies in consultation with the major professor. Coursework must include a minimum of 12 credits in physics graduate courses in the 700-999 levels (not including 711, 720, 721, or 990). A student may elect to complete one of the following minor programs: a minor of 9 to 12 credits in a single department; a minor of 12 credits In two or more departments. Traditional fields for the minor are mathematics, other natural sciences, computer sciences and engineering. In planning a minor in a single department, the student is advised by the minor professor; in planning a minor in two or more departments, the student is advised by the major professor. The program of study is to be chosen with the major professor and the departmental academic graduate committee.

##### Residence

The student must meet minimum Graduate School residence requirements.

##### Written Qualifying Examination

Prior to taking the oral doctoral preliminary examination, the student must pass a written qualifying examination which evaluates the student's general background in graduate-level physics. This examination is based on subject matter at least as advanced as the material covered by the non-thesis master's comprehensive examination. A student may not continue in the physics graduate program after 4.5 years without having passed this examination.

##### Doctoral Preliminary Examination and Doctoral Proposal Hearing

The student must prepare a written proposal and pass an oral examination to qualify for formal admission to candidacy for the degree. The oral examination primarily seeks to determine the student's preparation for independent research and the suitability of the proposed dissertation program. This examination shall be taken no later than four semesters after passing the written qualifying examination. However, no student will be required to take the oral examination earlier than the sixth semester of graduate work at UWM.

##### Dissertation

The candidate must present a dissertation reporting the results of an original and independent research investigation representing substantive creative contribution.

##### Dissertation Defense

The candidate must, as the final step toward the degree, pass an oral examination in defense of the dissertation.

##### Time Limit

All degree requirements must be completed within ten years from the date of initial enrollment in the doctoral program.

For additional information on the Ph.D., see the Graduate School Doctoral Requirements page.

#### Courses

*Courses numbered 300-699 are Undergraduate/Graduate. Courses numbered 700 and above are Graduate only.*

- 408 Experiments in Linear Electronics. 3 cr. U/G.
- Transistor and integrated circuit characteristics; electronic measurement and control. No cr for students w/cr in ElecEng 330(R). Prereq: jr st; Physics 210(P).

- 411 Mechanics. 4 cr. U/G.
- Kinematics, vector analysis, conservation laws, oscillations, variational methods, chaos, Lagrangian and Hamiltonian mechanics. Prereq: jr st; Physics 210(NP).

- 420 Electricity and Magnetism I. 3 cr. U/G.
- Electrostatics, capacitance, boundary value problems, mulipole expansion, dielectrics, magnetostatics, vector potential, magnetic properties of matter, motional emf, inductance, Maxwell's equations in differential form. Counts as repeat of 2 cr of Physics 421. Prereq: jr st; Physics 210(NP); a grade of B- or better in Math 321(P); or Math 321(P) and a grade of B- or better in Physics 370(P); or grad st.

- 422 Electricity and Magnetism II. 3 cr. U/G.
- Conservation laws in electrodynamics, Maxwell's stress tensor, electromagnetic waves, absorption, dispersion, reflection and transmission of plane electromagnetic waves, wave guides, retarded potentials, radiation, electrodynamics and relativity. Counts as repeat of 2 cr of Physics 421. Prereq: jr st, Physics 420(P); or grad st.

- 441 Introduction to Quantum Mechanics I. 4 cr. U/G.
- Historical background and experimental basis, De Broglie waves, correspondence principle, uncertainty principle, Schroedinger equation; hydrogen atom, electron spin, Pauli Principle, applications of wave mechanics. Prereq: jr st; Physics 309(NP); Math 321(C).

- 442 Introduction to Quantum Mechanics II. 3 cr. U/G.
- Continuation of Physics 441, emphasizing perturbation theory and applications to multi-electron systems, including atoms, molecules, and solids. Prereq: jr st; Physics 441(NP).

- 463 Introduction to Atmospheric Physics. 3 cr. U/G.
- Atmospheric phenomena not directly linked with the general circulation: refraction and scattering, visibility, radiation transfers, optics, aerosols and cloud particles, acoustics, radar, atmospheric electricity. Not available for grad cr at this time. Prereq: jr st; Physics 210(P), Math 232(P), or Atm Sci 350(P).

- 497 Study Abroad: (Subtitled). 1-12 cr. U/G.
- Designed to enroll students in UWM sponsored program before course work level, content, and credits are determined and/or in specially prepared program course work. Retakable w/chg in topic. Prereq: jr st; acceptance for Study Abroad Prog.

- 501 Special Topics: Mathematical Models of Physical Problems I. 3 cr. U/G.
- Selected topics in mathematics for study of the techniques and procedures for stating physical problems in mathematical terms and the physical interpretation of mathematical solutions. Prereq: jr st; Physics 210(P); Math 234(P).

- 502 Special Topics: Mathematical Models of Physical Problems II. 3 cr. U/G.
- More selected topics in mathematical models. Prereq: jr st; Physics 210(P); Math 234(P). Physics 501(R).

- 515 Statistical Mechanics. 3 cr. U/G.
- Brief survey of thermodynamics; statistical mechanics; classical and quantum gases. Prereq: jr st; Physics 317(P) & 441(P).

- 517 Special Relativity. 3 cr. U/G.
- Relativistic kinematics, the Lorentz transformation, tensor calculus, applications to motion of particles, electromagnetism. Prereq: jr st; Physics 411(R) & 421(R).

- 531 Principles of Quantum Mechanics I. 3 cr. U/G.
- Vector and Hilbert spaces; Schroedinger equation in 1, 2, and 3 dimensions; systems of many particles; symmetries; angular momentum. Prereq: jr st; Physics 441(P).

- 532 Principles of Quantum Mechanics II. 3 cr. U/G.
- Continuation of 531. Spin; hydrogen atom; variational methods; WKB approximation; perturbation theory; scattering theory; Dirac equation. Prereq: jr st; Physics 531(P).

- 541 Elementary Particles. 3 cr. U/G.
- Accelerators and detectors; special unitary groups; quark model of hadrons; Feynman diagrams; electromagnetic, weak and strong interactions of quarks and leptons; Higgs boson. Prereq: jr st; Physics 441(P).

- 551 Introduction to Solid State Physics I. 3 cr. U/G.
- Crystal structure, reciprocal lattice; crystal binding; elastic waves; phonons, lattice vibrations; thermal properties of insulators; free electron Fermi gas. Band structure; semiconductor crystals; Fermi surface. Prereq: jr st; Physics 441(P) or cons instr.

- 575 Vacuum Science and Technology. 3 cr. U/G.
- Viscous and molecular flow, vacuum materials and seals, metal-to-ceramic seals, evaporation and vapor pressures, vacuum pumps, vacuum gauges, mass spectrographs, chemical reactions at surfaces, outgassing. Prereq: jr st; Physics 441(P).

- 610 The Art and Science of Teaching Physics. 1 cr. U/G.
- Participants critique lectures, videotapes of experienced teachers, each other; address conceptual problems facing beginning students; gain familiarity with demonstrations, classroom technology; discuss their own classes. Prereq: appt as undergrad TA or grad st.

- 651 Introduction to Solid State Physics II. 3 cr. U/G.
- Transport, superconductivity, dielectric properties, ferroelectric crystals, magnetism, magnetic resonance, optical phenomena in insulators, nanostructures, non-crystalline solids, point defects, alloys, dislocations. Prereq: jr st; Physics 551(P).

- 670 Electron Microscopy Laboratory. 3 cr. U/G.
- Diffraction, imaging, and spectroscopy methods for study of morphology, crystallinity, and composition of solids in a transmission electron microscope. Prereq: sr st; Physics 551(P) or cons instr.

- 698 Research Experience for Teachers. 1-6 cr. U/G.
- Enrichment of students' physics background. Work with faculty mentor to develop an innovative teaching program for use in students' own classroom. Open only to practicing science teachers with demonstrable expertise in physics. May be retaken to 9 cr max. Prereq: sr st; current teaching contract.

- 705 Molecular, Cellular, and System Biophysics. 3 cr. G.
- Cell structure and the molecular basis for life. Molecular and cellular interactions. Supracellular organization, signalling, and communication. Self-similarity and cooperativity. Prereq: grad st

- 706 Biophotonics. 3 cr. G.
- Biophotonics and bioimaging; overview of application of optics in biology and medicine based on the understanding of basic optics, spectroscopy, and imaging theory. Prereq: grad st

- 707 Structural Molecular Biophysics. 3 cr. G.
- Methods in molecular biophysics. Prereq: grad st; major in science-based discipline & Physics 210(P), or writ cons instr.

- 711 Theoretical Physics-Dynamics. 3 cr. G.
- Lagrange equations, canonical formulation, principle of least action, normal coordinates, rigid bodies, special relativity, mathematical methods. Prereq: grad st; Math 321(C) or 322(C); or 701(C) or 702(C).

- 716 Advanced Topics in Statistical Physics. 3 cr. G.
- Systems of interactir particles; critical phenomena; transport theory; irreversible processes and fluctuations; model calculations for interacting systems of particles. Prereq: grad st; Physics 515(P), 532(P).

- 717 Gravitation. 3 cr. G.
- General theory of relativity. Metric, covariant derivative, and curvature. Einstein field equations. Newtonian and weak-field limits. Gravitational waves. Experimental tests. Black holes and relativistic stars. Prereq: grad st; Physics 517(P).

- 718 White Dwarfs, Neutron Stars, and Black Holes. 3 cr. G.
- Physics of compact objects; newtonian and relativistic stellar structure and stability; pulsars, x-ray sources; accretion disks; gravitational collapse; stellar-size and supermassive black holes; quasars. Prereq: grad st; Physics 717(P) or cons instr.

- 720 Electrodynamics I. 3 cr. G.
- Maxwell's equations; Helmholz theorem; scalar and vector potentials; boundary value problems; plane wave solutions. Prereq: grad st; Physics 711(P).

- 721 Electrodynamics II. 3 cr. G.
- Wave guides, radiation by charges; radiation reaction; radiation scattering, damping and dispersion; covariant formulation of electrodynamics. Prereq: grad st; Physics 720(P).

- 731 Quantum Mechanics. 3 cr. G.
- Mathematical formalism of quantum mechanics. Obserables and transformation theory, scattering perturbation, other approximation methods. Prereq: grad st; Physics 532(P) & 711(P).

- 732 Quantum Mechanics. 3 cr. G.
- Continuation of 731 including symmetry properties, relativistic quantum mechanics, introduction to the theory of quantized fields. Prereq: grad st & Physics 731(P).

- 735 High Energy Physics. 3 cr. G.
- Special relativity applied to high energy collisions, experimental techniques, ionization and radiation at high energy, weak interactions theory, II-meson and strange particle interactions, ultra-high energy phenomena. Prereq: grad st & Physics 732(P).

- 751 Solid State Theory I. 3 cr. G.
- Phonons, plasmons, magnons, fermion fields and the hartree-fock approximation, and electron many-body techniques and the electron gas. Prereq: grad st; Physics 531(P) & Physics 651(P).

- 752 Solid State Theory II. 3 cr. G.
- Dynamics of electrons in a magnetic field: energy bands, cyclotron resonance, impurity states, optical absorption and excitons in semiconductor crystals; electrodynamics of metals; green's functions. Prereq: grad st & Physics 532(P) & 751(P).

- 770 Electron Microscopy. 3 cr. G.
- Kinematical and dynamical theory of electron diffraction. Transfer function theory of imaging. Electron and x-ray spectroscopies. Applications to surfaces and interfaces. Prereq: grad st; Physics 551(P) or cons instr.

- 775 Surface Physics I. 3 cr. G.
- Survey of experimental techniques in surface physics research. Prereq: grad st; Physics 515(P) & 575(P).

- 781 Medical Radiation Physics. 3 cr. G.
- Physical principles of the generation, interaction, detection, and measurement of radiation in medical applications; basics of radiation protection. Prereq: grad st

- 782 Physics of Medical Imaging. 3 cr. G.
- Basic theoretical knowledge of the physics of diagnostic radiology using x-rays, magnetic resonance, nuclear medicine, and ultrasounds. Prereq: grad st

- 784 Radiotherapy Physics. 3 cr. G.
- Radiation physics for work as a hospital physicist, including accelerators for radiation therapy, quality characteristics of treatment beams, treatment planning, treatment techniques, quality assurance, oncology. Prereq: grad st

- 786 Medical Physics Practicum. 3 cr. G.
- Training with clinical medical imaging and therapy equipment, and dosimetry instrumentation. Prereq: grad st; Physics 781(P)

- 801 Special Topics in Theoretical Physics: (Subtitled). 2-3 cr. G.
- Discussion of recent research or advanced special topics. Retakable w/chg in topic to 9 cr max. Prereq: grad st & cons instr.

- 807 Group Theory and Its Applications to Physics. 3 cr. G.
- Representations of discrete and continuous groups, including rotation groups, unitary groups and crystal point and space groups. Symmetries of elementary particles. Molecular obitals, energy bands. Counts as repeat of Math 807. Prereq: grad st; Physics 532(P).

- 811 Nonlinear Dynamics and Chaos. 3 cr. G.
- Iteration of maps, numerical integration, strange attractors in dissipative systems, fractal dimensions, multifractals, entropy. Chaos in hamiltonian systems, perturbation theory, kam theorem. Quantum choas. Prereq: grad st; Physics 711(P).

- 817 Gravitation and Cosmology II. 3 cr. G.
- Experimental tests in gravitation. Gravitational waves: generation, detection. Spinning black holes. Cosmology: idealised cosmologies; present state of the universe; nucleosynthesis; inflation; recent developments. Prereq: grad st; Physics 717(P) or cons instr.

- 818 Advanced Topics in Gravitational Physics. 3 cr. G.
- Topics depend on student interest. Initial value problem. Spinors and positive mass. Singularity theorems. Modern kaluza-klein theory. Approaches to quantum gravity. Prereq: grad st; Physics 717(P).

- 831 Quantum Field Theory I. 3 cr. G.
- Group theory, canonical and path integral quantization, feynman rules, quantum electrodynamics, renormalization, quantum chromodynamics, electroweak theory, spontaneous symmetry breaking. Prereq: grad st; Physics 732(P).

- 851 Experimental Techniques in Low Temperature Physics. 3 cr. G.
- A survey of cooling techniques and temperature measurements at low temperatures. Prereq: grad st; cons instr.

- 852 Superconductivity. 3 cr. G.
- Properties of type I and type II superconductors, bcs and ginzburg-landau theory, vortices, and flux dynamics. Prereq: grad st; Physics 532(P) & 651(P).

- 853 Superfluidity. 3 cr. G.
- Bose-Einstein condensation. Properties of superfluid 4HE, 3HE and 3HE-4HE mixtures. Prereq: grad st; Physics 551(P) & 651(P) or physics 515(P).

- 854 Electron Phonon Interaction. 3 cr. G.
- Wave propagation in metals. Interaction of electrons with the lattice in normal metals, superconductors, and magnetic materials. Prereq: grad st; Physics 532(P) & 651(P).

- 900 Colloquium. 1 cr. G.
- Lectures by staff and visitors on research in various areas of physics. Prereq: grad st.

- 903 Seminar in Theoretical Physics: (Subtitled). 1-3 cr. G.
- Discussion of special topics of interest to research students in theoretical physics.Retakable w/chg in topic to 9 cr max. Prereq: grad st & cons instr.

- 904 Seminar in Surface Studies: (Subtitled). 1-3 cr. G.
- Special topics in the chemistry and physics of surface studies. Specific topics and any additional prerequisites announced in Timetable each time course is offered. Retakable w/chg in topic to 9 cr max. Prereq: grad st; cons instr.

- 905 Seminar in Solid State Physics: (Subtitled). 1-3 cr. G.
- Special topics in electron phonon interaction. Retakable w/chg in topic to 9 cr max. Prereq: grad st; Physics 551(P).

- 990 Research. 1-9 cr. G.
- Prereq: grad st & cons instr.

- 999 Independent Reading. 1-3 cr. G.
- For the benefit of graduate students unable to secure needed content in regular courses. Prereq: grad st, cons instr.