Results for PHYSICS

What sets quantum information apart from its classical counterpart is that it can be encoded non-locally, woven into correlations among multiple qubits in a phenomenon known as entanglement. We will discuss paradigms for harnessing entanglement to solve hitherto intractable computational problems or to push the precision of sensors to their fundamental quantum mechanical limits. We will also examine challenges that physicists and engineers are tackling in the laboratory today to enable the quantum technologies of the future.

How did the present Universe come to be? The last few decades have seen remarkable progress in understanding this age-old question. Course will cover the history of the Universe from its earliest moments to the present day, and the physical laws that govern its evolution. The early Universe including inflation and the creation of matter and the elements. Recent discoveries in our understanding of the makeup of the cosmos, including dark matter and dark energy. Evolution of galaxies, clusters, and quasars, and the Universe as a whole. Implications of dark matter and dark energy for the future evolution of the cosmos. Intended to be accessible to non-science majors, material is explored quantitatively with problem sets using basic algebra and numerical estimates.

How do the discoveries since the dawn of the 20th century impact our understanding of 21st-century physics? This course introduces the foundations of modern physics: Einstein's theory of special relativity and quantum mechanics. Combining the language of physics with tools from algebra and trigonometry, students gain insights into how the universe works on both the smallest and largest scales. Topics may include atomic, molecular, and laser physics; semiconductors; elementary particles and the fundamental forces; nuclear physics (fission, fusion, and radioactivity); astrophysics and cosmology (the contents and evolution of the universe). Emphasis on applications of modern physics in everyday life, progress made in our understanding of the universe, and open questions that are the subject of active research. Physical understanding fostered by peer interaction and demonstrations in lecture, and interactive group problem solving in discussion sections. Prerequisite: PHYSICS 23 or PHYSICS 23S.

Guided hands-on and simulation-based exploration of concepts in modern physics, including special relativity, quantum mechanics and nuclear physics with an emphasis on student predictions, observations and explanations. Pre- or corequisite: PHYSICS 25.

What is electricity? What is magnetism? How are they related? How do these phenomena manifest themselves in the physical world? The theory of electricity and magnetism, as codified by Maxwell's equations, underlies much of the observable universe. Students develop both conceptual and quantitative knowledge of this theory. Topics include: electrostatics; magnetostatics; simple AC and DC circuits involving capacitors, inductors, and resistors; integral form of Maxwell's equations; electromagnetic waves. Principles illustrated in the context of modern technologies. Broader scientific questions addressed include: How do physical theories evolve? What is the interplay between basic physical theories and associated technologies? Discussions based on the language of mathematics, particularly differential and integral calculus, and vectors. Physical understanding fostered by peer interaction and demonstrations in lecture, and discussion sections based on interactive group problem solving. Prerequisite: PHYSICS 41, 41E or equivalent. MATH 21 or MATH 51 or CME 100 or equivalent. Recommended corequisite: MATH 52 or CME 102. Please make sure your AP scores are uploaded before enrollment opens.

Hands-on exploration of concepts in electricity, magnetism, and circuits. Introduction to multimeters, function generators, oscilloscopes, and graphing techniques. Pre- or corequisite: PHYSICS 43.

(Third in a three-part series: PHYSICS 61, PHYSICS 71, PHYSICS 81.) This course recasts the foundations of electricity and magnetism in a way that will surprise, delight, and challenge students who have already encountered the subject at a college or AP level. Suitable for students contemplating a major in Physics or Engineering Physics, those interested in a rigorous treatment of physics as a foundation for other disciplines, or those curious about powerful concepts like transformations, symmetry, and conservation laws. Electrostatics and Gauss' law. Electric potential, electric field, conductors, image charges. Electric currents, DC circuits. Moving charges, magnetic field as a consequence of special relativity applied to electrostatics, Ampere's law. Solenoids, transformers, induction, AC circuits, resonance. Displacement current, Maxwell's equations. Electromagnetic waves. Throughout, we'll see the objects and theorems of vector calculus become manifest in charges, currents, and electromagnetic fields. Prerequisite: A score of 5 on the AP Physics C E&M exam or Physics 43; Physics 61; and Math 52 or Math 62CM. Recommended prerequisite: Physics 71. Corequisite: Math 53 or Math 63CM. This course was offered as PHYSICS 63 prior to Academic Year 2022-2023.

How do we draw conclusions about fundamental physics from experimental data? This course covers basic data analysis techniques and practical statistics used in experimental and computational physics research. Weekly Python-based labs will allow students to explore topics including data visualization, error propagation, evaluating hypotheses, and fitting analytical models. These labs incorporate real and simulated data from existing experiments such as a gamma-ray telescope and a detector that searches for dark matter. Students will learn to use Python libraries running in Jupyter Notebooks to analyze data and will, for example, study the rate at which the universe is expanding using existing data from multiple telescopes. No prior coding experience is required. Pre-requisite: Physics 61.

Designed for undergraduate physics majors but is open to all students with a calculus-based physics background and some laboratory and coding experience. Students make and analyze observations using the telescopes at the Stanford Student Observatory. Topics covered include navigating the night sky, the physics of stars and galaxies, telescope instrumentation and operation, imaging techniques, quantitative error analysis, and effective scientific communication. The course concludes with an independent project where student teams propose and execute an observational astronomy project of their choosing, using techniques learned in class to gather and analyze their data, and presenting their findings in the forms of professional-style oral presentations and research papers. Suggested preparation: Physics 89L. Enrollment by permission. Due to physical limitations at the observatory, this class has a firm enrollment cap. We may not be able to accommodate all requests to enroll. Before permission numbers are given students must complete this form: https://forms.gle/KDarBRcZWJZG3qr66.

Have you ever wanted to dream up a research question, then design, execute, and analyze an experiment to address it, together with a small group of your fellow students? This is an accelerated, guided experimental research experience, resembling real frontier research. Phenomena that have been studied include the magnetization of ferromagnets, the quantum hall effect in graphene, interference in superconducting circuits, loss in nanomechanical resonators, and superfluidity in helium. But most projects pursued (drawn from condensed matter and recently also particle physics) have never been done in the class before. Our equipment and apparatus for Physics 108 are very flexible, and not standardized like in most other lab classes. We provide substantial resources to help your team. Often, with instructors' help, students obtain unique samples from Stanford research groups. Prerequisite: PHYSICS 104, or other experience in electronics. Suggested but less critical: Physics 130 (many phenomena you might study build on quantum mechanics) and Physics 106 (experience with data analysis and useful measurement tools: lock-in amplifier, spectrum analyzer.) We recommend taking this class in junior year if possible, as it can inform post-graduation decisions and can empower the professor to write a powerful letter of recommendation.

The course will focus on the theory of functions of a complex variable - with broad implications in many areas of physics. As time allows, we will also cover the basics of group theory and the theory of group representations, with focus on symmetry groups that arise in various physical settings. Prerequisites: MATH 53 or equivalent and Physics 111 or the equivalent.

Numerical methods for solving problems in mechanics, astrophysics, electromagnetism, quantum mechanics, and statistical mechanics. Methods include numerical integration; solutions of ordinary and partial differential equations; solutions of the diffusion equation, Laplace's equation, and Poisson's equation with various methods; statistical methods including Monte Carlo techniques; matrix methods and eigenvalue problems. A short introduction to Python, which is used for class examples and active learning notebooks. Independent class projects allow deep explorations of course topics and make up a significant component of the course grade. No prerequisites but some previous programming experience is advisable.

Conservation laws and electromagnetic waves, Poynting's theorem, tensor formulation, potentials, and fields. Plane-wave problems (free space, conductors and dielectric materials, boundaries). Dipole and quadruple radiation. Special relativity and transformation between electric and magnetic fields. Prerequisites: PHYS 120 and PHYS 111 or MATH 131P or MATH 173;

The origins of quantum mechanics and wave mechanics. Schr¿dinger equation and solutions for one-dimensional systems. Commutation relations. Generalized uncertainty principle. Time-energy uncertainty principle. Separation of variables and solutions for three-dimensional systems; application to a hydrogen atom. Spherically symmetric potentials and angular momentum eigenstates. Spin angular momentum. Addition of angular momentum. Prerequisites: (PHYSICS 65 or PHYSICS 70 or PHYSICS 71) and (PHYSICS 111 or MATH 131P or MATH 173 or MATH 220) and PHYSICS 120.

Elementary particles and the fundamental forces. Quarks and leptons. The mediators of the electromagnetic, weak and strong interactions. Interaction of particles with matter; particle acceleration, and detection techniques. Symmetries and conservation laws. Bound states. Decay rates. Cross sections. Feynman diagrams. Introduction to Feynman integrals. The Dirac equation. Feynman rules for quantum electrodynamics and for chromodynamics. Undergraduates register for PHYSICS 152. Graduate students register for PHYSICS 252. (Graduate students will be required to complete additional assignments in a format determined by the instructor.) Prerequisite: PHYSICS 130.

What do we know about the physical origins, content, and evolution of the Universe -- and how do we know it? Students learn how cosmological distances and times, and the geometry and expansion of space, are described and measured. Composition of the Universe. Origin of matter and the elements. Observational evidence for dark matter and dark energy. Thermal history of the Universe, from inflation to the present. Emergence of large-scale structure from quantum perturbations in the early Universe. Astrophysical tools used to learn about the Universe. Big open questions in cosmology. Undergraduates register for Physics 161. Graduates register for Physics 261. (Graduate students will be required to complete additional assignments in a format determined by the instructor.) Prerequisite: PHYSICS 120 or equivalent.

Mean-field theory of phase transitions; critical exponents. Ferromagnetism, the Ising model. The renormalization group. Dynamics near equilibrium: Brownian motion, diffusion, Boltzmann equations. Other topics are at the discretion of the instructor. Prerequisite: PHYSICS 170. Recommended pre- or corequisite: PHYSICS 130.

Introduction to the properties of solids. Crystal structures and bonding in materials. Momentum-space analysis and diffraction probes. Lattice dynamics, phonon theory and measurements, thermal properties. Electronic structure theory, classical and quantum; free, nearly-free, and tight-binding limits. Electron dynamics and basic transport properties; quantum oscillations. Properties and applications of semiconductors. Reduced-dimensional systems. Undergraduates should register for PHYSICS 172 and graduate students for APPPHYS 272. Prerequisites: PHYSICS 170 and PHYSICS 171, or equivalents.

Undergraduate research in experimental or theoretical physics under the supervision of a faculty member. The faculty member will prepare a list of goals and expectations at the start of the research. The student will prepare a written summary of research accomplished by the end. Prerequisites: superior work as an undergraduate Physics major and consent of instructor.

Long-term experimental or theoretical project and thesis in Physics under supervision of a faculty member. Planning of the thesis project is recommended to begin as early as middle of the junior year. Successful completion of a senior thesis requires a minimum of 3 units for a letter grade completed during the senior year, along with the other formal thesis and physics major requirements. Students doing research for credit prior to senior year should sign up for Physics 190. Prerequisites: superior work as an undergraduate Physics major and approval of the thesis application.

This course will cover order of magnitude or approximate, low-tech approaches to estimating physical effects in various systems. One goal is to promote a synthesis of understanding of basic physics (including quantum mechanics, electromagnetism, and physics of fluids) through solving various classic problems. Another goal will be to learn how to decide which terms in complicated equations can be omitted or simplified - and to obtain general features of the solution without solving them in their full complexity. We will be applying techniques such as scaling and dimensional analysis - with the overarching goal to develop physical intuition.

Basis for higher level courses on atomic solid state and particle physics. Problems related to measurement theory and introduction to quantum computing. Approximation methods for time-independent and time-dependent perturbations. Semiclassical and quantum theory of radiation, second quantization of radiation and matter fields. Systems of identical particles and many electron atoms and molecules. Prerequisite: PHYSICS 230.

Elementary particles and the fundamental forces. Quarks and leptons. The mediators of the electromagnetic, weak and strong interactions. Interaction of particles with matter; particle acceleration, and detection techniques. Symmetries and conservation laws. Bound states. Decay rates. Cross sections. Feynman diagrams. Introduction to Feynman integrals. The Dirac equation. Feynman rules for quantum electrodynamics and for chromodynamics. Undergraduates register for PHYSICS 152. Graduate students register for PHYSICS 252. (Graduate students will be required to complete additional assignments in a format determined by the instructor.) Prerequisite: PHYSICS 130.

What do we know about the physical origins, content, and evolution of the Universe -- and how do we know it? Students learn how cosmological distances and times, and the geometry and expansion of space, are described and measured. Composition of the Universe. Origin of matter and the elements. Observational evidence for dark matter and dark energy. Thermal history of the Universe, from inflation to the present. Emergence of large-scale structure from quantum perturbations in the early Universe. Astrophysical tools used to learn about the Universe. Big open questions in cosmology. Undergraduates register for Physics 161. Graduates register for Physics 261. (Graduate students will be required to complete additional assignments in a format determined by the instructor.) Prerequisite: PHYSICS 120 or equivalent.

Curricular practical training for students participating in an internship with a physics-related focus. Meets the requirements for curricular practical training for students on F-1 visas. Prior to the internship, students submit a concise description of the proposed project and work activities. After the internship, students submit a summary of the work completed and skills learned, including a reflection on the professional growth gained as a result of the internship. This course may be repeated for credit. Students are responsible for arranging their own internship/employment and faculty sponsorship. Register under faculty sponsor's section number.

Study of the literature of any special topic. Preparation, presentation of reports. If taken under the supervision of a faculty member outside the department, approval of the Physics chair required. Prerequisites: 25 units of college physics, consent of instructor.

Designed for physics graduate students but open to all graduate students with a calculus-based physics background and some laboratory and coding experience. Students make and analyze observations using the telescopes at the Stanford Student Observatory. Topics covered include navigating the night sky, the physics of stars and galaxies, telescope instrumentation and operation, imaging and spectroscopic techniques, quantitative error analysis, and effective scientific communication. The course concludes with an independent project where student teams propose and execute an observational astronomy project of their choosing, using techniques learned in class to gather and analyze their data, and presenting their findings in the forms of professional-style oral presentations and research papers. Enrollment by permission. To get a permission number please complete form: https://forms.gle/KDarBRcZWJZG3qr66 form. If you have not heard from us by the beginning of class, please come to the first class session.

Required of graduate students. May be repeated for credit.

Theory of renormalization. The renormalization group and applications to the theory of phase transitions. Renormalization of Yang-Mills theories. Applications of the renormalization group of quantum chromodynamics. Perturbation theory anomalies. Applications to particle phenomenology. Prerequisite: PHYSICS 331.

This course provides an overview of the Standard Model of Particle Physics, motivations for extending the Standard Model (including naturalness, the hierarchy, the cosmological constant, and strong CP problems), discussions on Technicolor and Composite Models, Grand Unified Theories and SU(5), exploration of the Supersymmetric Standard Model (including gauge coupling unification and lessons from LEP and the LHC), re-evaluation of naturalness, the multiverse, and the landscape of string theory, as well as topics such as split supersymmetry, string theory, large extra dimensions, the strong CP problem, and the QCD axion.

Intended to complement PHYSICS 361, this course will cover the earlier period in cosmology up to and including nucleosynthesis. The focus will be on high energy, early universe physics. This includes topics such as inflation and reheating including generation of density perturbations and primordial gravitational waves, baryogenesis mechanisms, out of equilibrium particle production processes in the early universe e.g. both thermal and non-thermal production mechanisms for dark matter candidates such as WIMPs and axions, and production of the light nuclei and neutrinos. Techniques covered include for example out of equilibrium statistical mechanics such as the Boltzmann equation, and dynamics of scalar fields in the expanding universe. Other possible topics if time permits may include cosmological phase transitions and objects such as monopoles and primordial black holes. We will use quantum field theory, although it will hopefully be accessible for those without much background in that area. Suggested prerequisites: general relativity at the level of PHYSICS 262, some knowledge of cosmology and in particular the basics of FRW cosmology as in PHYSICS 361 for example, and some knowledge of quantum field theory e.g. at the level of PHYSICS 331 as a corequisite.

Modern astrophysics explores physical processes in remote environments that prescribe, apply, and explore fundamental processes under conditions that are far more extreme than those attainable in a terrestrial laboratory. These include the production and interaction of peta eV gamma rays, peta eV neutrinos, and zetta eV cosmic rays by black holes and the behavior of 100 giga Tesla magnetic field anchored by neutron stars. The connection between observations, experiments, and the underlying physics will be emphasized. This course is intended for graduate students but should be accessible to advanced undergraduates. An understanding of basic general relativity and introductory quantum electrodynamics will be helpful but is not essential.

Superfluidity and superconductivity. Quantum magnetism. Prerequisite: PHYSICS 372.

This course describes the origin and the present status of inflationary cosmology. The main topics include: The Big Bang theory and the theory of cosmological phase transitions. Formation of domain walls, cosmic strings, and monopolies. Problems of the Big Bang theory, and solving these problems in inflationary cosmology. Main conceptual steps: Starobinsky model, old inflation, new inflation, chaotic inflation, eternal inflation. Reheating of the universe after inflation. Inflationary perturbations and the large-scale structure formation. Inflationary gravitational waves. Popular inflationary models such as hybrid inflation, natural inflation, Higgs inflation, and alpha-attractors. Testing inflationary models. Theory of tunneling and stochastic approach to inflation. The problem of initial conditions. Inflation in supergravity and string theory. Wave function of the universe, quantum cosmology, multiverse, and string theory landscape. Suggested prerequisites: general relativity at the level of PHYSICS 262 and some knowledge of quantum field theory at the level of PHYSICS 331.

Many body quantum systems can display rich dynamical phenomena far from thermal equilibrium. Understanding the non-equilibrium dynamics of quantum matter represents an exciting research frontier at the interface of condensed matter and AMO physics, high energy theory and quantum information. This is particularly topical in light of experimental advances in building quantum simulators and intermediate-scale quantum computers, which naturally operate in far-from-equilibrium regimes. This course is intended to serve as an introduction to this active research area, assuming only a knowledge of quantum mechanics and statistical physics. Topics covered include: quantum thermalization, quantum chaos, many-body localization, quantum entanglement and its dynamics, Floquet theory and time crystals, quantum circuits, quantum simulation, and tensor network methods. Prerequisites: PHYSICS 113, PHYSICS 130, PHYSICS 131, PHYSICS 170, and PHYSICS 171.

Open only to Physics graduate students, with consent of instructor. Work is in experimental or theoretical problems in research, as distinguished from independent study of a non-research character in 190 and 293.