Physics

PHYSICS 5000 Independent Work

Prerequisites: senior standing and apply for approval using the Physics independent study web form https://physics.wustl.edu/independent-study. Program and credit to be determined; maximum 6 units.

Credit 6 units.

Typical periods offered: Fall, Spring

PHYSICS 5010 Theoretical Physics

The first part of a two-semester course reviewing the mathematical methods essential for the study of physics. Theory of functions of a complex variable, residue theory; review of ordinary differential equations; introduction to partial differential equations; integral transforms.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5011 Mechanics

Motion of a point particle, rotational motion, oscillation, gravitation and central forces, Lagrangian and Hamiltonian formulation.

Credit 3 units. A&S IQ: NSM Art: NSM

Typical periods offered: Spring

PHYSICS 5020 Methods of Theoretical Physics II

Continuation of Physics 5010. Introduction to function spaces; self-adjoint and unitary operators; eigenvalue problems, partial differential equations, special functions; integral equations; introduction to group theory.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5021 Electricity and Magnetism I

Starting from Coulomb's law, the Biot-Savart law, and Faraday's law, the electrical and magnetic fields are defined and applied. Maxwell's equations are derived and their consequences, such as electromagnetic waves and relativity, are explored.

Credit 3 units. A&S IQ: NSM, AN BU: SCI

Typical periods offered: Fall

PHYSICS 5022 Electricity and Magnetism II

The second course in a two part series covering the classical theory of electricity and magnetism leading to the derivation and application of Maxwell's equation. Topics in electrodynamics including Faraday's law, the displacement current and Maxwell's equations in vacuum and in matter are covered. Electromagnetic waves and radiation, special relativity and relativistic electrodynamics will also be discussed.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5027 Introduction to Computational Physics

What does it mean to solve a research problem using a computer? What is the difference between someone ran a simulation and an interesting research result? And what skills does it take? Familiarity with a programming language is, of course, essential, but that is only the beginning. This course will focus on the methodology of computational research, touching also on topics in numerical analysis, statistics and visualization. The format will combine lectures and hands-on experience, with emphasis on research-style small-group projects.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall

PHYSICS 5035 Nuclear and Radiochemistry Lab

Application of radiochemistry to problems in chemistry, physics, and nuclear medicine, with emphasis on particle detectors and experimental techniques. Prerequisites: 3 units of physical chemistry or quantum mechanics, or permission of instructor. Five hours of laboratory a week.

Credit 3 units. A&S IQ: NSM Art: NSM

PHYSICS 5050 Classical Electrodynamics I

Classical electromagnetism via Maxwell's equations. Electric and magnetic fields from static charge and current distributions. Mathematical techniques for solving electrostatic and magnetostatic problems. Electrostatic and magnetostatic forces and energies.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5054 Physics of Living Systems

One of the grand challenges in contemporary biophysics is placing our understanding of cellular systems on a firm quantitative footing. How does the collective activity of molecules enable the cell to sense its environment, make decisions, grow and develop? This course, aimed at physical and life science students, will serve as an introduction to the physical principles and mathematical techniques underlying the analysis of systems and synthetic biology. Topics will include modeling gene and signaling networks, the regulation of intracellular structures, and pattern formation in development. Students in this course can expect to learn both analytical and computer simulation approaches to fundamental problems in biology, biophysics, and biotechnology. This course is for Graduate students ONLY.

Credit 0 units.

Typical periods offered: Fall, Spring

PHYSICS 5060 Classical Electrodynamics II

Time-varying electric and magnetic fields. Electromagnetic waves and radiation; simple antennas. Waveguides and effects of dispersion. Retardation effects and special relativity.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5063 Statistical Mechanics and Thermodynamics

Basic methods of classical and quantum statistical mechanics, thermodynamics, and transport theory.

Credit 3 units. A&S IQ: NSM, AN

Typical periods offered: Fall

PHYSICS 5068 Introduction to Quantum Information

A general introduction to the field of quantum information: physics of information processing, quantum logic, quantum algorithms, physical hardware for quantum computation, quantum communications, quantum error corrections, quantum sensing. An independent research project under the instructor's supervision is required.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5070 Classical Mechanics

The culminating achievements in this classical discipline are presented: the Lagrangian and Hamiltonian formulation of the equations of motion, action principles and the Hamilton-Jacobi equation. Applications to constrained systems, many-body systems, continuous systems and classical fields are included. Perturbation theory and general relativity are discussed briefly.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5071 Quantum Mechanics

Origins of quantum theory, wave packets and uncertainty relations, Schroedinger's equation in one dimension, step potentials and harmonic oscillators, eigenfunctions and eigenvalues, Schroedinger's equation in three dimensions, the hydrogen atom, symmetry, spin and the periodic table, approximation methods for time independent problems, quantum statistics. This section is for Graduate students ONLY.

Credit 3 units. A&S IQ: NSM Art: NSM

PHYSICS 5072 Solid State Physics

Crystal structures, binding energies, thermal properties, dielectrics, magnetism, free electron theory of metals, band theory, semiconductors, defects in solids. This course is for Graduate students ONLY.

Credit 3 units. A&S IQ: NSM Art: NSM

Typical periods offered: Spring

PHYSICS 5074 Introduction to Particle Physics

Introduction to the standard model of particle physics, including symmetries, conservation laws, the weak interaction, the strong interaction, quark confinement, and some more exotic ideas such as grand unified theories. This course is for Graduate students ONLY.

Credit 3 units. A&S IQ: NSM, AN Art: NSM

Typical periods offered: Spring

PHYSICS 5078 From Black Holes to the Big Bang

An introduction to general relativity. The goal will be to illustrate important features of general relativity without the full-blown mathematics of Einstein's equations by restricting attention to spherically symmetric spacetimes. Topics will include: principle of equivalence; curved spacetime; spherical stars and black holes; the Big Bang model, observational cosmology. 

Credit 3 units. A&S IQ: NSM Art: NSM

Typical periods offered: Spring

PHYSICS 5080 Artificial Intelligence and Machine Learning Methods With Applications to Physics

The course will introduce key ideas of AI and machine learning from a statistical physics perspective. Essentials of statistical distributions, kernel methods, neural networks, large language models, diffusion models, and many other tools will be presented from this physics based approach. Students will apply these techniques to problems in physics. Apart from the very first assignments, nearly all homework problems will assume the use of Python. If you do not know Python, there will be an additional very brief introduction to Python that the instructor will give in addition to the course lectures. This course is for Graduate students ONLY.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5090 Nonlinear Dynamics

The course will treat the theoretical foundations of nonlinear dynamics, and its applications to phenomena in diverse fields including physics, biology, and chemistry. Topics will include phase plane analysis, stability analysis, bifurcations, chaos, and iterated maps.

Credit 3 units.

Typical periods offered: Fall, Spring

PHYSICS 5230 Quantum Mechanics I

Provides a rigorous introduction to quantum mechanics with an emphasis on formalism. The course begins with review of the theory of linear (state) vector spaces and the quantum theory of measurement. Topics covered include dynamics of quantized systems, the quantum theory of angular momentum, density matrix formalism, and advanced topics in quantum measurement theory.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5240 Quantum Mechanics II

Review of wave mechanics, scattering theory. Measurement algebra and the foundations of nonrelativistic quantum theory. Mathematical techniques for solution, perturbation theory. Applications to atomic, molecular, nuclear, and solid state problems. Introduction to relativistic quantum theory and quantized wave fields.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5290 Statistical Mechanics

Gibbs' formalism of statistical mechanics and applications to thermodynamics. Quantum statistical mechanics and degenerate matter. General theory of equilibrium including phase transitions and critical phenomena. Interacting particles including non-ideal gases, ferromagnetism, and superconductivity. Transport theory, irreversible processes.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5300 Advanced Topics in Statistical Mechanics

Critical phenomena and renormalization group theory: scaling, universality, exact solutions, series expansions, computer simulations, e-expansion. Role of solitons and instantons in phase transitions. Quantum fluids: superfluidity and superconductivity. Linear response theory and disordered systems.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5321 Electronic Laboratory

Credit 3 units.

PHYSICS 5322 Physical Measurement Laboratory

A variety of classical and modern experiments in physics, including five experiments in nuclear radiation. Use of computers in experiment control, data acquisition, and data analysis. Development of skills in writing lab notebooks and formal reports and giving short oral presentations on experiments. Two laboratory periods each week.

Credit 3 units. A&S IQ: NSM, AN, WI Art: NSM BU: SCI

Typical periods offered: Fall

PHYSICS 5330 Planets and Life in the Universe

In this course, we will explore the history, methods, outcomes, and broad impacts of exoplanet research and how these are connected to our search for life beyond planet Earth. Following an engaging contextual introduction at the beginning of the lectures, topics will be presented with an accessible mathematical treatment (e.g., geometrical derivations of the two-body transit problem). 

Credit 3 units. A&S IQ: NSM, AN Art: NSM

Typical periods offered: Fall

PHYSICS 5370 Kinetics of Materials

A general discussion of phase formation and phase transformation in solids and liquids. Topics include equilibrium and non-equilibrium thermodynamics, equilibrium and metastable phase diagrams, nucleation and growth, spinodal transformations, diffusion and interface limited processes, shear type transformations and order/disorder transformations.  A background in thermodynamics, statistical mechanics, and solid state physics is strongly recommended.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5400 Quantum Theory of Many-Particle Systems

Develops a modern approach to quantitative microscopic description of strongly-interacting quantum many-particle systems, including the helium liquids, nuclear matter, neutron star matter, nuclei, and strongly-coupled electron systems. Emphasis is placed on the method of self-consistent Green's functions. Diagram resummation and field theoretic techniques are introduced. Applications are discussed that cover the Hartree-Fock method for atoms, Bose-Einstein condensation of atoms, etc. The microscopic basis for pairing in superfluids and superconductors is also examined.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5420 Physics of Finite and Infinite Nuclear Systems

Quantum mechanics of finite and infinite systems of protons and neutrons. Interaction between nucleons. Independent-particle model of nuclei and shell structure. Contrast with atomic shell model. Isospin symmetry. Information from weakly and strongly interacting probes of nuclei. Nuclear decay properties and some historical context. Many-particle description of nuclear systems. Single-particle versus collective phenomena. Properties of excited states. Bulk properties of nuclei. Nuclear and neutron matter. Role of different energy scales in determining nuclear properties: influence of long-range, short-range, and medium-induced interactions. Pairing correlations in nuclear systems. Relevance of nuclear phenomena and experiments for astrophysics and particle physics. This course is for Graduate students ONLY.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5430 Group Theory and Symmetries in Physics

Symmetries offer beautiful explanations for many otherwise incomprehensible physical phenomena in nature. Group theory is the underlying mathematical framework for studying symmetries, with far-reaching applications in many areas of physics, including solid-state physics, atomic and molecular physics, gravitational physics, and particle physics. We will discuss many of the fascinating mathematical aspects of group theory while highlighting its physics applications. The following topics will be covered: general properties of groups (definition, subgroups and cosets, quotient group, homo- and iso-morphism), representation theory (general group actions, direct sums and tensor products, Wigner-Eckart theorem, Young tablelaux), and discrete groups (cyclicity, characters, examples), Lie groups and Lie algebra (Cartan-Weyl basis, roots and weights, Dynkin diagrams, Casimir operators, Clebsch-Gordan coefficients, classification of simple Lie algebras), space-time symmetries (translation and rotation, Lorentz and Poincare groups, conformal symmetry, supersymmetry and superalgebra), and gauge symmetries (Abelian and non-Abelian, Standard Model, Grand Unified Theories).

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5440 Superconductivity

This course introduces the theory and phenomena of superconductivity, from its experimental discovery to modern microscopic theories and applications. Students will earn both the phenomenological descriptions (London equations, Ginzburg–Landau theory) and the microscopic foundations (Cooper pairing, BCS theory, electron–phonon interactions). Special emphasis will be given to applications such as superconducting magnets, RF cavities, and quantum devices, as well as extensions to unconventional superconductors.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5460 Galactic Astrophysics

In these lectures, the focus is on the dynamics and statistical mechanics of a collection of stars, which is treated as a collisionless system. The course begins with a discussion of potential theory and proceeds to discuss the density and phase distributions of stars in star clusters and galaxies, thus leading to an understanding of the equilibria and stability of these systems. Topics such as Chandrasekhar's dynamical friction, galaxy formation and dark matter will constitute the final topics of discussion.

Credit 3 units. A&S IQ: NSM Art: NSM BU: SCI

Typical periods offered: Fall

PHYSICS 5470 Intro to Elementary Particle Physics

An introduction to the standard model of elementary particle physics. The non-Abelian SU() X SU(2) X U (1) gauge theory and its relation to phenomenology and experiments.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5490 Solid State Physics I

Quantum theory of phonons in solids, thermodynamical properties, band theory of solids, free-electron and tight-binding approaches to electronic structure.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5500 Solid State Physics II

Band magnetism and local moments, Ising models, electron-electron and electron-phonon interactions, superconductivity.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5505 Quantum Hardware

An introduction to hardware used in quantum information processing, including superconducting qubits, trapped ions, neutral atoms, solid state spins, quantum defects for sensing, quantum photonics for communications, topological qubits, etc.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5510 Relativistic Quantum Mechanics

Introduction to Quantum Field Theory using simple 1-dimensional and/or scalar field examples. Canonical quantization and path integrals; Feynman diagrams; Lorentz group; discrete symmetries; LSZ theorem. Introduction to regularization and renormalization.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5520 Relativistic Quantum Field Theory

Continuation of Phys 551. Path integral quantization of spin 1/2 and spin 1 fields. Quantum electrodynamics. Ward identities and renormalization. Computation of the electron anomalous magnetic moment and the Lamb shift. Non-Abelian gauge theories and their quantization. Quantum chromodynamics and asymptotic freedom. Spontaneous symmetry breaking and the Standard Model.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5550 Modern Astrophysics

This course will describe the astronomical objects and physical processes that constitute modern astrophysics. It will begin with white dwarfs, neutron stars, black holes and accretion discs and jets. Next will come the phenomena that these objects produce: novae, pulsars, supernovae, quasars, radio sources, relativistic particles, and cosmic rays. This will be followed with calculations of essential physical processes, including coherent radio emission, synchrotron radiation, pair production and particle acceleration. It will conclude with discussions of open questions: what makes supernovae, the properties of pulsars, the origin of fast radio bursts. The choice of questions will respond to student interests.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5560 Stellar Astrophysics

In the second semester, the focus is on the dynamics and statistical mechanics of a collection of stars which is treated as a collisionless system. The course begins with a discussion of potential theory and proceeds to discuss the density and phase space distributions of stars in star clusters and galaxies, thus leading to an understanding of the equilibria and stability of these systems. Topics such as Chandrasekhar's dynamical friction and dark matter will constitute the final topics of discussion. 

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5570 Gravitation and Cosmology

Special relativity, equivalence principle, and fundamental experiments. Mathematics of curved spacetime. General structure of Einstein's equations. Observational tests. Applications of general relativity, relativistic stellar structure, gravitational collapse and black holes.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5580 Relativistic Astrophysics

Applications of general relativity to astrophysics and cosmology. Relativistic stars, gravitational collapse and black holes; generation, propagation and detection of gravitational radiation. Cosmology, the Standard Model; physical processes in the early universe and the microwave background. Inflationary scenario. Origin of galaxies and large-scale structure. Gravitational lenses. Credit 3 units.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5590 Testing Fundamental Physics With Astronomical Observations

Astronomical observations allow us to test fundamental physics laws under more extreme conditions than possible in terrestrial laboratories. In some important cases (i.e. cosmology), astronomical observations present the only way to gather empirical evidence and to formulate and subsequently test the theories. In this one-semester course, we start with a brief summary of the current theoretical framework that is used to explain the cosmos: the theory of General Relativity and the Standard Model of particle physics. Subsequently, we introduce current astronomical observatories and discuss which fundamental physics laws they can probe. We include a detailed discussion of theoretical ideas which are being probed, and avenues for developing more precise tests with future experiments. This class is designed to be highly relevant for theoretical and experimental researchers. Previous exposure to the theory of General Relativity and quantum field theories is beneficial but not required.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5600 X-Ray and Gamma-Ray Astrophysics

This course provides an introduction to the field of X-ray and Gamma-ray Astrophysics in the context of the wider field of High-Energy Astrophysics, which elucidates the information derivable from investigations of cosmic rays, radio waves, x-rays, gamma-rays, and gravitational waves emitted by astronomical sources.  Physical processes such as acceleration of particles to highly relativistic energies in astrophysical plasmas, synchrotron radiation, inverse-Compton scattering, bremsstrahlung, Cerenkov emission, dispersion and Faraday rotation of radio waves are discussed in the context of modeling the astrophysical sources.  The physics underlying supernovae, supernova remnants, pulsars, powerful radio, x-ray and gamma-ray sources, active galactic nuclei, quasars and the recently discovered gravitational wave sources powered by coalescing binary black holes, and neutron stars constitutes the main body of this course.  The subject of dark matter in the galaxies is briefly touched upon.  The design of detectors for carrying out the observations is also briefly presented.  

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5630 Topics in Theoretical Biophysics

What can Deep Learning teach us about the Brain? What can Artificial Intelligence in Neural Networks teach us about the functioning of Natural Intelligence in Brains? What can Computational Neuroscience teach us about the functioning of Artificial Intelligence in Neural Networks? Do the mechanisms of Artificial Intelligence in deep networks serve as a framework for the investigation of Natural Intelligence in evolved brains? Deep Neural Networks (DNNs) have revolutionized Machine Learning and Artificial Intelligence. These networks have recently found their way back into computational neuroscience. DNNs reach human-level performance in certain tasks. Importantly, DNNs can display certain characteristics of brain function that cannot be captured with shallow handcrafted models. With this, DNNs offer an intriguing novel framework that may enable computational neuroscientists to address fundamental questions concerning complexity and neural computation in brains. In this course we will evaluate the tantalizing hypothesis that DNNs can serve as a tool to understand aspects of brain function, thus moving closer towards an understanding of both, natural and artificial intelligence. The course will be organized around 15 key papers illustrating major ideas of DNNs and computational neuroscience. Background material will be provided.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5680 Astrostatistics

The course will be centered on astrostatistics and explore fundamental concepts in statistics and computer science, using astrophysics as the basis of application. The course will introduce the essential principles and techniques of astrostatistics, equipping students with the necessary tools to analyze and interpret data from various astrophysical phenomena, while the methods covered will also apply to problems outside of astronomy.

Credit 3 units.

Typical periods offered: Fall, Spring, Summer

PHYSICS 5810 Critical Analysis of Scientific Data

Data science is most commonly associated with topics in computer science. But efficient algorithms, specific software packages, neural nets, etc., are only tools, and are easily misused. In a research setting, working with data is primarily an exercise in critical thinking. The purpose of this interactive, hands-on course is to learn from mistakes by making them in a safe environment. After covering/reviewing probability theory; Bayesian inference; elements of information theory and random matrix theory, the course will focus on case studies of real-world biological data, such as quantitative imaging data, next generation sequencing (metagenomics), and neural recordings. These modules will involve critical reading of research papers and working through puzzle-based assignments. The primary modules will be supplemented by shorter presentations on topics chosen by students. Fair warning: this is explicitly NOT a course on big data or machine learning, although students may choose to explore some of these topics in their presentations (required for credit). Experience with MatLab or Python strongly encouraged or will need to be acquired during the course. 

Credit 3 units.

Typical periods offered: Fall, Spring

PHYSICS 5820 Research Seminar

Designed to introduce students to current developments in physics and to research carried out by faculty. Topics vary each year. Each member of the department addresses issues in their particular specialty. Required of all  first-year graduate students. 

Credit 1 unit.

Typical periods offered: Fall

PHYSICS 5840 Computational Methods

This course provides an introduction to the computational techniques that are most widely used in both theoretical and experimental research in physics. Each lecture will use a realistic research problem to introduce the algorithms, software packages and numerical techniques that will be used by the students to develop a solution on the computer. Topics include Monte Carlo techniques, symbolic analysis with Mathematica, data acquisition software used in the laboratory, the numerical solution of quantum mechanical problems, and an introduction to general purpose frameworks based on Python.

Credit 1 unit.

Typical periods offered: Spring

PHYSICS 5890 Selected Topics in Physics I

From time to time, additional courses are offered in specialized physics topics of current interest, such as group theory, general relativity, advanced hydrodynamics, boundary-value problems, celestial mechanics, astrophysics, and so on.

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5900 Selected Topics in Physics II

From time to time, additional courses are offered in specialized topics of current interest such as group theory, general relativity, advanced hydrodynamics, boundary-value problems, celestial mechanics, astrophysics, etc.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5930 Introduction to Methods in Physics

Five hours per week of tutorial training in modern experimental and/or theoretical methods in physics. Instruction by faculty members or, with faculty supervision and assistance by graduate teaching interns. 

Credit 3 units.

Typical periods offered: Fall

PHYSICS 5940 Introduction to Methods in Physics

Five hours per week of tutorial training in modern experimental and/or theoretical methods in physics. Instruction by faculty members or, with faculty supervision and assistance, by graduate teaching interns who are enrolled in and earning credit for Phys 597-598. A maximum of 3 units of this course may be counted toward the requirement of 36 units of course credit for the Ph.D. degree.

Credit 3 units.

Typical periods offered: Spring

PHYSICS 5970 Supervised Teaching of Physics

Teaching is an integral part of your career development as a physicist. Whether you pursue a career in academia, become a researcher, or work in industry, you will need to teach others. This discussion-based course is designed to engage first-year graduate students in discussions about the science teaching and learning, with a major emphasis on insights and experimental evidence from cognitive psychology and education research.

Credit 1 unit.

Typical periods offered: Fall

PHYSICS 5980 Supervised Teaching of Physics

Supervised instructional experience as a graduate teaching intern. Under faculty supervision, a teaching intern may earn credit in Phys 597-598 by (a) instructing graduate students who are taking Phys 593-594, or (b) instructing undergraduates who are taking Phys 241-242 or 341-342 or 441-442, or (c) as a Graduate Teaching Fellow or Assistant, instructing and evaluating work of undergraduate or graduate students in classroom and laboratory physics courses, or (d) instructional activity connected with journal club, group seminars, special short courses, observatory lectures, etc. Five or more contact hours per week with student(s) being instructed, plus associated preparation and evaluation.

Credit 1 unit.

Typical periods offered: Fall, Spring