Twin Cities campus

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Twin Cities Campus

Physics Minor

School of Physics & Astronomy
College of Science and Engineering
Link to a list of faculty for this program.
Contact Information
Director of Graduate Studies in Physics, School of Physics and Astronomy, University of Minnesota, 116 Church St. SE, Minneapolis, MN 55455 (612-626-5982; fax: 612-624-4578)
Email: grad@physics.umn.edu
Website: http://www.physics.umn.edu/grad
  • Program Type: Graduate minor related to major
  • Requirements for this program are current for Fall 2017
  • Length of program in credits (master's): 6
  • Length of program in credits (doctoral): 12
  • This program does not require summer semesters for timely completion.
Physics is the study of the fundamental structure and interactions of matter. Research areas in the program include experimental and theoretical studies in astrophysics and cosmology, biological physics, condensed matter physics, elementary particle physics, nuclear physics, space and planetary physics, and physics education research. Interdisciplinary study is also available with the programs in astrophysics, biological sciences, chemistry, chemical engineering and materials science, electrical and computer engineering, mechanical engineering, and the history of science and technology.
Program Delivery
  • via classroom (the majority of instruction is face-to-face)
Prerequisites for Admission
Other requirements to be completed before admission:
A physics minor requires a background in differential and integral calculus and one year of calculus-level college physics.
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
Use of 4xxx courses toward program requirements is permitted under certain conditions with adviser approval.
The master's minor requires a minimum of 6 credits in PHYS courses (including 5001 or 5012). The doctoral minor requires a minimum of 12 credits in PHYS courses (including 5001 and 5002-or-5011 and 5012). The following courses cannot be used to satisfy the requirements: Physics 4001, 4002, 4101, 4201, and 4303.
Elective Course Options
PHYS subject requirements can be met through a combination of any of the classes listed below (minimum 2 credits for MS minor after required course and minimum 4 credits for PhD minor after required courses)
Take 2 or more credit(s) from the following:
Atomic Physics and Optics
· PHYS 8161 - Atomic and Molecular Structure (3.0 cr)
· Biophysics and Medical Physics
· PHYS 5081 - Introduction to Biopolymer Physics (3.0 cr)
or PHYS 5401 {Inactive} (4.0 cr)
or PHYS 5402 {Inactive} (4.0 cr)
or PHYS 8311 - Biological Physics of Single Molecules (3.0 cr)
or PHYS 8312 - Biological Physics of Macroscopic Systems (3.0 cr)
or PHYS 8300 - Seminar: Biological and Medical Physics. (1.0 cr)
· Condensed Matter Physics
· PHYS 4211 - Introduction to Solid-State Physics (3.0 cr)
or PHYS 5701 - Solid-State Physics for Engineers and Scientists (4.0 cr)
or PHYS 8702 - Statistical Mechanics and Transport Theory (3.0 cr)
or PHYS 8711 - Solid-State Physics I (3.0 cr)
or PHYS 8712 - Solid-State Physics II (3.0 cr)
or PHYS 8750 - Advanced Topics in Condensed Matter Physics (3.0 cr)
or PHYS 8700 - Seminar: Condensed Matter Physics (1.0 cr)
· Elementary Particle Physics
· PHYS 4511 - Introduction to Nuclear and Particle Physics (3.0 cr)
or PHYS 8011 - Quantum Field Theory I (3.0 cr)
or PHYS 8012 - Quantum Field Theory II (3.0 cr)
or PHYS 8013 - Special Topics in Quantum Field Theory (3.0 cr)
or PHYS 8901 - Elementary Particle Physics I (3.0 cr)
or PHYS 8902 - Elementary Particle Physics II (3.0 cr)
or PHYS 8911 - Introduction to Supersymmetry (3.0 cr)
or PHYS 8950 {Inactive} (3.0 cr)
or PHYS 8900 - Seminar: Elementary Particle Physics (1.0 cr)
· Mathematical, Advanced Quantum, and Computational Physics
· PHYS 5041 - Mathematical Methods for Physics (4.0 cr)
or PHYS 5042 {Inactive} (4.0 cr)
or PHYS 8001 - Advanced Quantum Mechanics (3.0 cr)
or PHYS 8301 - Symmetry and Its Application to Physical Problems (3.0 cr)
· Nuclear Physics
· PHYS 8800 - Seminar: Nuclear Physics (1.0 cr)
or PHYS 8801 - Nuclear Physics I (3.0 cr)
or PHYS 8802 - Nuclear Physics II (3.0 cr)
or PHYS 8850 - Advanced Topics in Nuclear Physics (3.0 cr)
· Plasma and Space Physics
· PHYS 4611 - Introduction to Space Physics (3.0 cr)
or PHYS 4621 - Introduction to Plasma Physics (3.0 cr)
or PHYS 8601 - Plasma Physics I (3.0 cr)
or PHYS 8602 - Plasma Physics II (3.0 cr)
or PHYS 8611 - Cosmic Rays and Plasma Astrophysics (3.0 cr)
or PHYS 8650 - Advanced Topics in Space and Plasma Physics (3.0 cr)
or PHYS 8600 - Seminar: Space Physics (1.0 cr)
· Relativity and Cosmology
· PHYS 5022 - Relativity, Cosmology, and the Universe (4.0 cr)
or PHYS 8501 - General Relativity and Cosmology I (3.0 cr)
or PHYS 8502 - General Relativity and Cosmology II (3.0 cr)
or PHYS 8200 - Seminar: Cosmology and High Energy Astrophysics (1.0 cr)
· Physics Education
· PHYS 5072 - Best Practices in College Physics Teaching (1.0-3.0 cr)
or PHYS 8100 - Seminar: Problems of Physics Teaching and Higher Education (1.0 cr)
Program Sub-plans
Students are required to complete one of the following sub-plans.
Students may not complete the program with more than one sub-plan.
Masters
Students must complete a minimum of 6 credits in physics including either Physics 5001 or 5011.
Required Courses
PHYS 5001 - Quantum Mechanics I (4.0 cr)
or PHYS 5011 - Classical Physics I (4.0 cr)
Doctoral Minor
Students must complete a minimum of 12 credits in physics, including either the classical physics sequence or the quantum mechanics sequence.
Required Courses
Quantum Mechanics Sequence
PHYS 5001 - Quantum Mechanics I (4.0 cr)
PHYS 5002 - Quantum Mechanics II (4.0 cr)
or Classical Physics Sequence
PHYS 5011 - Classical Physics I (4.0 cr)
PHYS 5012 - Classical Physics II (4.0 cr)
 
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PHYS 8161 - Atomic and Molecular Structure
Credits: 3.0 [max 3.0]
Grading Basis: A-F only
Typically offered: Fall Odd Year
Emphasizes interpretation of quantum numbers and selection rules in terms of symmetry. Experimental data summarized and compared with theoretical predictions. prereq: Level of mathematics associated with BS in physical sciences
PHYS 5081 - Introduction to Biopolymer Physics
Credits: 3.0 [max 3.0]
Course Equivalencies: Phys 4911/5081
Typically offered: Every Spring
Introduction to biological and soft condensed matter physics. Emphasizes physical ideas necessary to understand behavior of macromolecules and other biological materials. prereq: PHYS 2201 or equivalent
PHYS 8311 - Biological Physics of Single Molecules
Credits: 3.0 [max 3.0]
Typically offered: Spring Odd Year
Biological molecules, based on statistical mechanics, kinetics, optics, and other physics ideas. Physics of DNA/proteins, their interactions. Force spectroscopy (optical tweezers, atomic force microscopy). Concepts of optical spectroscopy. Single molecule fluorescence/imaging. prereq: [[5201 or Chen 4707], 5011] or instr consent
PHYS 8312 - Biological Physics of Macroscopic Systems
Credits: 3.0 [max 3.0]
Typically offered: Spring Even Year
Macroscopic systems, based on physics such as fluid dynamics, statistical mechanics, non-linear dynamics, and chaos theory. Super-molecular aggregates. Biological physics of the cell. Biological physics of populations/evolution. prereq: [[5201 or CHEN 4707], 5011] or instr consent
PHYS 8300 - Seminar: Biological and Medical Physics.
Credits: 1.0 [max 6.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
Current research in biological and medical physics prereq: instr consent
PHYS 4211 - Introduction to Solid-State Physics
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
A modern presentation of the properties of solids. Topics include vibrational and electronic properties of solids; diffraction of waves in solids and electron band structure. Other possible topics include optical properties, magnetic phenomena, and superconductivity. prereq: 2201, 4101
PHYS 5701 - Solid-State Physics for Engineers and Scientists
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall & Spring
Crystal structure and binding; diffraction; phonons; thermal and dielectric properties of insulators; free electron model; band structure; semiconductors. prereq: Grad or advanced undergrad in physics or engineering or the sciences
PHYS 8702 - Statistical Mechanics and Transport Theory
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Equilibrium properties of macroscopic classical and quantum systems. Phase transitions and Renormalization Group. Transport theory. Applications to soft condensed matter systems. prereq: 5201 or instr consent
PHYS 8711 - Solid-State Physics I
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Fundamental properties of solids. Electronic structure and transport in metals and semiconductors. Properties of disordered materials. prereq: 4211, 5002 or instr consent
PHYS 8712 - Solid-State Physics II
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Fundamental properties of solids. Electronic structure and transport in metals and semiconductors. Properties of disordered materials. prereq: 8711 or instr consent
PHYS 8750 - Advanced Topics in Condensed Matter Physics
Credits: 3.0 [max 9.0]
Typically offered: Periodic Fall & Spring
Sample research topics: magnetism, superconductivity, low temperature physics, superfluid helium. prereq: 8712 or instr consent
PHYS 8700 - Seminar: Condensed Matter Physics
Credits: 1.0 [max 6.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
Current research. prereq: instr consent
PHYS 4511 - Introduction to Nuclear and Particle Physics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Fundamental particles and Standard Model. Symmetries/quarks, models of nuclei, interactions between particles/nuclei, tests of conservation laws, fission/fusion. prereq: 4101
PHYS 8011 - Quantum Field Theory I
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Second quantization of relativistic wave equations: canonical quantization of the free scalar and Dirac fields. Fields in interaction: interaction picture. Quantum electrodynamics: quantization of the electromagnetic field, propagators and Feynman rules, tree-level processes. Higher-order processes and renormalization. prereq: 8001 or instr consent
PHYS 8012 - Quantum Field Theory II
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Aspects of general theory of quantized fields, including space-time and discrete transformation properties, the CPT theorem, and the spin-statistics connection. Introduction to functional and path-integral methods. Renormalization group and asymptotic freedom. Semi-classical methods and instantons in gauge theories. prereq: 8011 or instr consent
PHYS 8013 - Special Topics in Quantum Field Theory
Credits: 3.0 [max 3.0]
Typically offered: Spring Even Year
Includes non-perturbative methods in quantum field theory, supersymmetry, two-dimensional quantum field theories and their applications, lattice simulations of quantum fields, topological quantum field theories, quantum field theory methods applied to condensed matter physics, and string theory. prereq: 8012 or instr consent
PHYS 8901 - Elementary Particle Physics I
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Types of fundamental interactions. Exact and approximate symmetries and conservation laws. Gauge quanta: gluons, photons, W and Z bosons, gravitons. Fundamental fermions: leptons and quarks. Isotopic and flavor SU(3) symmetries of strong interaction. Heavy hadrons. Amplitudes and probabilities. Quantum chromodynamics. prereq: 8001 or instr consent
PHYS 8902 - Elementary Particle Physics II
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Deep inelastic scattering. Weak interactions of leptons. Semileptonic and nonleptonic weak processes with hadons. Oscillations of neutral Kaons. Violation of CP symmetry in Kaons. Neutrino masses and oscillations. Standard model of the electroweak interaction. Grand unification. Unitarity of the S matrix. Properties of soft pions. prereq: 8901 or instr consent
PHYS 8911 - Introduction to Supersymmetry
Credits: 3.0 [max 3.0]
Grading Basis: A-F only
Typically offered: Spring Even Year
Motivation. Coleman-Mandula theorem. Supersymmetric Quantum Mechanics. 4D supersymmetry algebra and representations. Extended supersymmetry. N=1 superspace and superfields. Supersymmetric guage theories. Chiral/vector multiplets. Non-renormalization theorems. Supersymmetry breaking. Supersymmetric Standard Model. Phenomenology. Nonperturbative supersymmetry. Supergravity. prereq: 8011 or instr consent
PHYS 8900 - Seminar: Elementary Particle Physics
Credits: 1.0 [max 6.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
Elementary particle physics, high energy physics, particle astrophysics and cosmology.
PHYS 5041 - Mathematical Methods for Physics
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Survey of mathematical techniques needed in analysis of physical problems. Emphasizes analytical methods. prereq: 2601 or grad student
PHYS 8001 - Advanced Quantum Mechanics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Topics in non-relativistic quantum mechanics; second quantization. Introduction to Diagrammatic and Green's function techniques and to relativistic wave equations. Application of relativistic perturbation theory to particle interactions with electromagnetic field. Invariant interactions of elementary particles. prereq: 5002 or instr consent
PHYS 8301 - Symmetry and Its Application to Physical Problems
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Fundamental invariance principles obeyed by laws of physics. Group theory as tool for using symmetry and invariance to help understand behavior of physical systems. Applications made to atomic, molecular, nuclear, condensed-matter, and elementary particle physics. prereq: 5002 or instr consent
PHYS 8800 - Seminar: Nuclear Physics
Credits: 1.0 [max 6.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
Current research topics.
PHYS 8801 - Nuclear Physics I
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Nuclear/neutrino astrophysics. Thermonuclear reactions. Processes of nucleosynthesis. Origin of the elements. Stellar evolution. Theory of supernovae. Exotic stars. Chemical evolution of galaxies. prereq: 5001, 5002, 5011, 5012, 5201; AST 4001 recommended
PHYS 8802 - Nuclear Physics II
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Properties of nuclei based on hadronic and quark-gluon degrees of freedom. Relativistic field theory at finite temperatures and density applied to many-body problems, especially nuclear matter and quark-gluon plasma. Applications to lepton and hadron scattering, nucleus-nucleus collisions, astrophysics and cosmology. prereq: 8801 or instr consent
PHYS 8850 - Advanced Topics in Nuclear Physics
Credits: 3.0 [max 9.0]
Typically offered: Fall Odd Year
Research topics. prereq: 8802 or instr consent
PHYS 4611 - Introduction to Space Physics
Credits: 3.0 [max 3.0]
Typically offered: Fall Odd Year
Dynamics of charged particles/plasmas in space. Physics of the Sun and solar wind. Solar/galactic cosmic rays. Interactions of solar wind with planetary magnetospheres. Dynamics of Magnetosphere. Formation of the aurora. Physics of radiation belts. prereq: PHYS 4001, PHYS 4002
PHYS 4621 - Introduction to Plasma Physics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Basic properties of collisionless, magnetized plasmas, single particle motion, plasmas as fluids, magnetohydrodynamics, waves in plasmas, equilibrium, instabilities, kinetic theory/shocks. Prereq: PHYS 4001, PHYS 4002
PHYS 8601 - Plasma Physics I
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Theory of plasma waves and instabilities in plasmas, magnetohydrodynamics, nonlinear waves in plasmas, wave propagation in inhomogeneous plasmas. prereq: 4621, 5012 or instr consent
PHYS 8602 - Plasma Physics II
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Theory of plasma waves and instabilities, collisions, radiation, transport, nonlinear wave-particle and wave-wave interactions, instabilities in inhomogeneous plasmas. prereq: 8601 or instr consent
PHYS 8611 - Cosmic Rays and Plasma Astrophysics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Properties of energetic particles in heliosphere and in astrophysical environments; solar physics, including radiation and magnetic effects; solar wind and magnetospheric physics; physics of radiation belts. prereq: 5012 or instr consent
PHYS 8650 - Advanced Topics in Space and Plasma Physics
Credits: 3.0 [max 9.0]
Typically offered: Periodic Fall
Topics in plasma waves and instabilities, solar physics, cosmic ray physics, atmospheric physics or planetary physics. prereq: 8602 or 8611 or instr consent
PHYS 8600 - Seminar: Space Physics
Credits: 1.0 [max 6.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
Current topics in space physics and plasma physics.
PHYS 5022 - Relativity, Cosmology, and the Universe
Credits: 4.0 [max 4.0]
Course Equivalencies: Ast 5022/Phys 5022
Typically offered: Periodic Fall
Large-scale structure and history of universe. Introduction to Newtonian and relativistic world models. Physics of early universe. Cosmological tests. Formation of galaxies. prereq: 2601 or instr consent
PHYS 8501 - General Relativity and Cosmology I
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Tensor analysis and differential geometry. Special relativity leading to formulation of principles of general relativity and Einstein's equations. Tests of general relativity and thorough discussion of various black hole solutions, including Schwarzschild, Reissner-Nordstrom, and Kerr solutions. prereq: 5012 or instr consent
PHYS 8502 - General Relativity and Cosmology II
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Gravitational radiation. Applications of general relativity to stellar structure of white dwarfs and neutron stars, action principle, and symmetric spaces. Big-bang cosmology, strongly emphasizing particle physics. prereq: 8501 or instr consent
PHYS 8200 - Seminar: Cosmology and High Energy Astrophysics
Credits: 1.0 [max 6.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
Current topics in cosmology and high energy astrophysics. prereq: instr consent
PHYS 5072 - Best Practices in College Physics Teaching
Credits: 1.0 -3.0 [max 5.0]
Typically offered: Every Fall & Spring
Pedagogies for introductory physics classes. Topics from educational research/practice as applied to classroom.
PHYS 8100 - Seminar: Problems of Physics Teaching and Higher Education
Credits: 1.0 [max 3.0]
Typically offered: Every Spring
Lectures and informal discussions of courses and curricula, techniques, and materials important in undergraduate physics instruction; relation to general problems of higher education.
PHYS 5001 - Quantum Mechanics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Schrodinger equation: bound state and scattering problems in one dimension. Spherically symmetric problems in three dimensions, angular momentum, and the hydrogen atom. Approximation methods for stationary states. Time-dependent perturbation theory. Operators and state vectors: general formalism of quantum theory. prereq: 4101 or equiv or instr consent
PHYS 5011 - Classical Physics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Classical mechanics: Lagrangian/Hamiltonian mechanics, orbital dynamics, rigid body motion, special relativity. prereq: 4001, 4002 or instr consent
PHYS 5001 - Quantum Mechanics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Schrodinger equation: bound state and scattering problems in one dimension. Spherically symmetric problems in three dimensions, angular momentum, and the hydrogen atom. Approximation methods for stationary states. Time-dependent perturbation theory. Operators and state vectors: general formalism of quantum theory. prereq: 4101 or equiv or instr consent
PHYS 5002 - Quantum Mechanics II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Symmetry in quantum mechanics, space-time symmetries and the rotation group, Clebsch-Gordan coefficients and the Wigner-Eckart theorem. Scattering theory. Method of second quantization with elementary applications. Relativistic wave equations including Dirac equation. prereq: 5001 or equiv
PHYS 5011 - Classical Physics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Classical mechanics: Lagrangian/Hamiltonian mechanics, orbital dynamics, rigid body motion, special relativity. prereq: 4001, 4002 or instr consent
PHYS 5012 - Classical Physics II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Classical electromagnetism: electrostatics, magnetostatics, Maxwell's equations, electromagnetic waves, radiation, interaction of charged particles with matter. prereq: 5011 or instr consent