### CAS PY 501 Mathematical Physics

Introduction to complex variables and residue calculus, asymptotic methods, and conformal mapping; integral transforms; ordinary and partial differential equations; non-linear equations; integral equations.

### CAS PY 502 Computational Physics

Fundamental methods of computational physics and applications; numerical algorithms; linear algebra, differential equations; computer simulation; vectorization, parallelism, and optimization. Examples and projects on scientific applications.

### CAS PY 511 Quantum Mechanics I

General theory of quantum mechanics, including the Schrodinger, Heisenberg, and interaction pictures. The path integral formulation. Angular momentum: orbital and spin angular momentum, addition of angular momenta, Wigner-Eckart theorem. Scattering theory: time-independent, partial waves and phase shift, identical particles, time dependent, and propagators.

### CAS PY 512 Quantum Mechanics II

Continuation of CAS PY 511. Degenerate and nondegenerate perturbation theory. Second quantization of nonrelativistic systems with applications to scattering, lifetime of excited atomic states, many-body problems. Relativistic quantum mechanics: Klein-Gordon equation, Dirac equation.

### CAS PY 521 Electromagnetic Theory I

Vector and tensor analysis. Electrostatics, uniqueness, electrostatic energy, capacitance. Boundary value problems, conformal mapping, variable separation, Green's functions. Multipole expansion, electric polarization, atomic models, anisotropic media. Contour integration and application to frequency-dependent dielectric constant. Dielectrics, electrostatic energy, boundary value problems.

### CAS PY 536 Quantum Computing

Quantum physics as a powerful computational paradigm. Quantum bits (qubits), qubit operations and quantum gates, computation, and algorithms. Computational complexity classes, and efficiency of classical vs. quantum computers. Quantum Fourier transform and Shor's factorization algorithm. Physical implementation of quantum computation. Also offered as CAS CS 536.

### CAS PY 538 Interdisciplinary Methods for Quantitative Finance

Expands upon the foundations of finance theory with interdisciplinary approaches from statistical physics and machine learning. Equips the students with the Python tools to tackle a broad range of problems in quantitative financial analysis and combines the study of relevant financial concepts with computational implementations. Students learn to use packages like Numpy, Pandas, Statsmodels and Scikit, which are commonly used in research and in the industry.

### CAS PY 541 Statistical Mechanics I

Probability theory. Ensembles. Steepest descent methods. Paramagnetism, ideal gas, Einstein model, adsorption isotherms. Thermodynamics, Maxwell relations, heat capacity. Bose and Fermi gases. Electrons in metals, white dwarf stars, black-body radiation, phonons, Bose-Einstein condensation. Interacting systems, virial expansion, Van der Waals gas. Phase transitions: mean-field theories, spin systems.

### CAS PY 542 Statistical Mechanics II

Continuation of CAS PY 541; emphasis on applications. Phase transitions: thermodynamic theory of phase transitions, mean field theories (Landau theory). Fluctuations: equilibrium fluctuations, instabilities, fluctuation dissipation theories. Elementary kinetic theory: mean free path approach, Boltzmann equation. Stochastic mathematics: probability theory, Markoff processes, Gaussian processes. Brownian motion: Langevin equations, Fokker-Planck equation.

### CAS PY 543 Introduction to Solid State Physics

An introduction to crystal structure; lattice vibrations; electronic energy bands and Fermi surfaces; semiconductors, conductors, and insulators; superconductivity and magnetism.

### CAS PY 551 Introduction to Particle Physics

Fundamental particles and their symmetries. Isospin and flavor. Discrete symmetries. Phenomenology of weak and strong interactions. Introduction to detector techniques.

### CAS PY 555 Cosmological Physics

Early universe cosmology: inflation, thermodynamics in an expanding universe with radiation, matter, vacuum energy. Growth of density perturbations, cosmic microwave background, large scale structure. The cosmological standard model and open questions, dark matter, dark energy, neutrinos.

### CAS PY 559 Quantitative Microbiology

### CAS PY 565 Dynamics of Nonlinear Systems

Introduces the modern approach to the dynamics of nonlinear systems, which approach is often called "nonlinear science," a term that stresses the interdisciplinary applications of nonlinear dynamics that go well beyond classical mechanics to include examples from all the natural sciences, engineering, and even social sciences and medicine. Organized around three "paradigms" of nonlinear science: (1) chaos and fractals; 2) "solitons" and coherent structures; and 3) patterns and pattern selection and will involve analytical, computational, and experimental studies.

### CAS PY 571 Introduction to Biological Physics

Introduction to biomolecular forces, energy flow, information and thermodynamics in biological systems. Nucleic acid, protein, and biomembrane structure. Mechanisms of transport and signaling in biological membranes. Biophysical techniques including spectroscopy. Emphasis on the physical principles underlying biological structure and function.

### CAS PY 580 Machine Learning for Physicists

Machine learning is one of the most dynamic areas of modern research and application. This class provides an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists.

### CAS PY 581 Advanced Laboratory

Classical experiments in atomic and nuclear physics, development of new experiments, basic research projects. Experiments include magnetic resonance, nuclear-decay studies, Zeeman effect, holography, black-body radiation, X-ray diffraction, Mossbauer studies, and flux quantization, positron annihilation. Effective Fall 2018, this course fulfills a single unit in each of the following BU Hub areas: Writing-Intensive Course, Oral and/or Signed Communication, Research and Information Literacy.

### CAS PY 681 Electronics for Scientists

A survey of practical electronics for all College of Arts and Sciences science students wishing to gain a working knowledge of electronic instrumentation, and in particular, its construction. Two four-hour laboratory-lecture sessions per week. Effective Spring 2020 this course fulfills a single unit in each of the following BU Hub areas: Digital/Multimedia Expression, Creativity/Innovation, Research and Information Literacy.

### GRS PY 677 An Introduction to Evidence-Based Undergraduate STEM Teaching

Online course with in-person faculty-led sessions. Participants learn about effective teaching strategies and the research that supports them, and apply approaches to lesson design and assignments for future teaching opportunities. Also offered as GRS BI 677 and GRS CH 677.

### GRS PY 701 Advanced Mathematical Physics

Mathematical structures; algebraic systems, topological spaces, measure theory, and integration. Functional analysis: Banach and Hilbert spaces, linear functionals, operators, and spectral theory. Other applications at discretion of instructor.

### GRS PY 713 Quantum Field Theory I

Provides an introduction to the techniques of quantum field theory with applications to high-energy and condensed-matter physics. Topics include field equations and quantization of many-body systems; Green function and linear response theory; S-matrix and scattering theory; path integration; perturbation expansions and the Feynman rules; renormalization and effective field theories; epsilon expansion and critical exponents.

### GRS PY 714 Quantum Field Theory II

A continuation of GRS PY 713 for particle physicists. Topics include relativistic fields; LSZ formalism; the Lorentz group; quantum electrodynamics; non-Abelian gauge symmetry; spontaneous symmetry breaking; Goldstone's theorem; the Higgs mechanism; the Glashow-Weinberg-Salam model.

### GRS PY 731 Theory of Relativity

An introduction to general relativity: the principle of equivalence; Riemannian geometry; Einstein's field equation; the Schwarzschild solution; the Newtonian limit; experimental tests; black holes; cosmology.

### GRS PY 741 Solid-State Physics I

One electron band structure: Formalism: Hartree-Fock, density functional frameworks. Methods: Green function, pseudopotentials and tight binding. Linear response. Optical properties. Elastic properties. Phonons: lattice dynamics and phenomenological methods. Electronic instabilities and transitions. Topological aspects of band structure and topological phases.

### GRS PY 742 Solid-State Physics II

Many-body formalism: second quantization, Green function, perturbation theory, Feynman diagrams. BEC and superfluidity. Fermi liquids; Luttinger liquids, bosonization. Electron-phonon interactions and superconductivity. Quantum magnetism: exchange mechanisms; magnetic insulators, spin-wave theory; itinerant magnetism, spin-density waves. Magnetic impurities, Anderson model, Kondo effect.

### GRS PY 743 Low-Temperature Physics

Superconductivity, superfluidity, and properties of 3He and 4He at low temperatures. Techniques and measurement of physical quantities near absolute zero.

### GRS PY 744 Polymer Physics

Introduction to polymer physics, focusing on the structure, phase behavior, and dynamics of isolated chains, polymer solutions, and gels. Development of underlying theoretical formalism and comparison with experimental results. Discussion of applications to novel polymeric materials.

### GRS PY 745 Experimental Surface Physics and Chemistry

Introduction to the principles and experimental techniques of surface and interface physics and chemistry. Electronic, structural, vibrational, and magnetic properties of solid surfaces and interfaces. Emphasis on how these properties are measured. Also vacuum technology and x-ray generation.

### GRS PY 747 Advanced Statistical Mechanics

Introduction to classical and quantum chaos: Random Matrix Theory. Eigenstate thermalization hypothesis. Doubly-stochastic evolution. Fluctuation theorems and other thermodynamic relations. Integrable systems, Many-body localization. Dynamics of Hamiltonian systems close to the adiabatic limit. Counter-adiabatic driving. Non-adiabatic response and quantum geometry.

### GRS PY 751 High-Energy Physics 1

Yearlong course (with GRS PY 752) on phenomenological aspects of modern high-energy physics. Principal topics are the standard model of strong and electro-weak interactions and the physics of electro-weak symmetry breaking. Intended for both theoretical and experimental students; emphasis on current calculational techniques.

### GRS PY 752 High-Energy Physics 2

Yearlong course (with GRS PY 751) on phenomenological aspects of modern high-energy physics. Principal topics are the standard model of strong and electro-weak interactions and the physics of electro-weak symmetry breaking. Intended for both theoretical and experimental students; emphasis on current calculational techniques.

### GRS PY 771 Systems Biology for Physical Scientists and Engineers

Focus is modern work on modeling biochemical networks. Core material includes signaling, genetic switches, biological oscillators and development. Begins with chemical kinetics in the context of molecular biology. Simple yet informative models based on physics approaches are emphasized.

### GRS PY 782 Advanced Materials Characterization

Introduction to the principles and applications of advanced materials characterization including study of atomic structure, electronic structure, defects, mechanical properties, transport properties, and carrier dynamics.

### GRS PY 789 Computational Quantum Many-Body Physics

This course introduces computational techniques for lattice models of interacting fermions, bosons, and quantum spins. Methods include Lanczos diagonalization, matrix-product states, and quantum Monte Carlo methods. Applications are taken from condensed matter and quantum-device physics (e.g., quantum annealing).

### GRS PY 811 Advanced Quantum Field Theory

Covers Scale Invariant Theories and Conformal Invariant Theories in various dimensions with applications to quantum criticality, statistical physics, and high-energy physics.

### GRS PY 841 Symmetry in Condensed Matter Physics

Theories of finite groups and their irreducible representations (Irreps), symmetry projection operators. Product groups and product representations. Crystalline symmetry, symmorphic and non-symmorphic space groups and induction of their Irreps. Spin-1/2 double groups, magnetic color groups. Time-reversal symmetry and co-representations.

### GRS PY 895 Seminar: Special Topics in Theoretical Physics

Theoretical research topics include general relativity, quantum field theory, high energy and particle physics, phase transitions, renormalization group, laser physics, kinetic equations, biophysics, computational physics, and selected topics in mathematical physics.

### GRS PY 896 Seminar: Special Topics in Theoretical Physics

Theoretical research topics include general relativity, quantum field theory, high energy and particle physics, phase transitions, renormalization group, laser physics, kinetic equations, biophysics, computational physics, and selected topics in mathematical physics.

### GRS PY 897 Seminar: Special Topics in Experimental Physics

Surface physics; intermediate energy nuclear physics experiments; low temperature techniques; liquid and solid helium; and magnetism at low temperatures. Raman effect, gels, and biophysics. High-energy physics experimental techniques.

### GRS PY 898 Seminar: Special Topics in Experimental Physics

Surface physics; intermediate energy nuclear physics experiments; low temperature techniques, liquid and solid helium, and magnetism at low temperatures. Raman effect, gels, and biophysics. High-energy physics experimental techniques.

### GRS PY 903 Res in Phys 3

### GRS PY 961 Scholarly Methods in Physics 1

Introduction to scholarly methods in physics teaching and research: effective STEM instructional techniques; successful oral and written presentations; reading and reporting scientific literature; ethical obligations in physics teaching and research; career paths in physics. Required of first-semester doctoral students.

### GRS PY 962 Scholarly Methods in Physics 2

Continuation of GRS PY 961. Scholarly methods in physics teaching and research: reading and reporting scientific literature; ethical obligations in teaching and research; priority and other publication issues; career issues in physics. Required of second-semester doctoral students.