Results for APPLIED PHYSICS

This class introduces the basics of aeronautics and astronautics through applied physics, hands-on activities, and real world examples. The principles of fluid flow, flight, and propulsion for aircraft will be illustrated, including the creation of lift and drag, aerodynamic performance including takeoff, climb, range, and landing. The principles of orbits, maneuvers, space environment, and propulsion for spacecraft will be illustrated. Students will be exposed to the history and challenges of aeronautics and astronautics.

What is quantum physics and what makes it so weird? We'll introduce key aspects of quantum physics with an aim to explain why it differs from everyday 'classical' physics. Quantum-enabled devices like the laser and atomic clocks for GPS will be explained. We will also discuss the breakthroughs driving the 2nd quantum technology revolution surrounding quantum simulators, sensors, and computers. Seminar discussions and a laser lab will help illustrate core principles, including the atomic clock mechanism. Visits to campus laboratories will introduce cutting-edge quantum experiments. This IntroSem is designed for those likely to go on to major in the humanities or in a STEM program outside of the natural sciences. (Likely STEM majors are instead encouraged to take 100-level quantum courses upon completion of pre-requirements.) While basic familiarity with high school physics is recommended, qualitative explanations will be emphasized. By the end of the quarter, you will be able to explain the key tenets of quantum physics, how it has enabled current technology, and what new technologies might emerge from the 2nd quantum revolution.

Preference to freshmen. Exploration via case studies how functional materials have been developed and incorporated into modern devices. Particular emphasis is on magnetic and dielectric materials and devices. Recommended: high school physics course including electricity and magnetism.

Preference to frosh. Choices for meeting the future energy needs of the U.S. and the world. Basic physics of energy sources, technologies that might be employed, and related public policy issues. Trade-offs and societal impacts of different energy sources. Policy options for making rational choices for a sustainable world energy economy.

Students will create individual studio portfolios of ceramic work and pursue technical investigations of clay properties and the firing process using modern scientific equipment. Emphasis on development of creative process; parallels between science and traditional craft; integration of creative expression with scientific method and analysis. Prior ceramics experience desirable but not necessary. Limited enrollment. Prerequisites: any level of background in physics, Instructor permission.

Students will learn to weave on a table loom while examining textile structures from historic, artistic and scientific perspectives. Emphasis on analyzing patterns and structures generated by weaving, with elementary introductions to information-scientific notions of algorithmic complexity, image compression, and source coding. This class is primarily intended for non-STEM majors with little or no prior experience in working with textiles. Limited enrollment. Prerequisites: Instructor permission.

Preference to sophomores. Indigo as a plant, biomolecule, dye, ancient craft material, and organic semiconductor; the interest of natural dyes for both biomimetic engineering and indigenous artistic practices. Students will plant and tend an indigo crop, harvest and process indigo leaves for dyestuffs, and dye textiles using an organic vat process. Lectures, readings and discussions will focus on the biochemistry and physics of indigo dye, traditional indigo textile arts, environmental impacts of industrial-scale indigo dyeing of denim, roles of indigo in upcycling, craft-washing, and the aesthetics of indigo in western and non-western cultural frames.

Things sit at the nexus of cross-cutting heterogeneous processes; tracing the entanglements of any prominent thing or class of things demands a transdisciplinary approach that recruits expertise from the natural sciences, social sciences and humanities. For example, carbon is a key factor in global warming for reasons that are as much socio-historical as bio-physical, and we could not begin to sketch the full significance of carbon without considering such diverse frames of reference. Our growing appreciation in the social sciences and humanities of the agency, polyvalence and catalytic role of things has given rise to The New Materialist and Post-Humanist movements, which in turn raise questions about intra-action and observational perspective that are echoed in the modern physical and life sciences. In this class we will explore these theoretical convergences in considering themes such as `things-in-themselves¿, networks and open systems, assemblages and entanglements. We will also examine specific examples such as oil, metal (guns), dams, viruses, electricity, mushrooms; each thing will be explored both in terms of its social and ethical entanglements and in terms of its material properties and affordances. There will also be hands-on encounters with objects in labs and a couple of local field trips. The key question throughout will be `why and how does matter matter in society today?

Students explore the use of Stanford Nano Shared Facilities (SNSF) for physical analysis of material samples of interest for art conservation, technical art history and archaeology. Weekly SNSF demonstrations will be supplemented by lectures on intellectual context by Stanford faculty/staff and conservators from the Fine Arts Museums of San Francisco (FAMSF). Students will undertake analysis projects derived from ongoing conservation efforts at FAMSF, including training on the use of relevant SNSF instruments and data analysis.

Applied Physics Core course appropriate for graduate students and advanced undergraduate students with prior knowledge of elementary quantum mechanics, electricity and magnetism, and special relativity. Interaction of electrons with intense electromagnetic fields from microwaves to x- ray, including electron accelerators, x-ray lasers and synchrotron light sources, attosecond laser-atom interactions, and x-ray matter interactions. Mechanisms of radiation, free-electron lasing, and advanced techniques for generating ultrashort brilliant pulses. Characterization of electronic properties of advanced materials, prospects for single-molecule structure determination using x-ray lasers, and imaging attosecond molecular dynamics.

Applied Physics Core course appropriate for graduate students and advanced undergraduate students with prior knowledge of elementary quantum mechanics, electricity and magnetism, and ordinary differential equations. Structure of single- and multi-electron atoms and molecules, and cold collisions. Phenomenology and quantitative modeling of atoms in strong fields, with modern applications. Introduction to quantum optical theory of atom-photon interactions, including quantum trajectory theory, mechanical effects of light on atoms, and fundamentals of laser spectroscopy and coherent control.

Applied Physics Core course appropriate for graduate students and advanced undergraduate students with prior knowledge of elementary quantum mechanics. Introduction to materials and topics of current interest. Topics include superconductivity, magnetism, charge and spin density waves, frustration, classical and quantum phase transitions, multiferroics, and interfaces. Prerequisite: elementary course in quantum mechanics.

Core course appropriate for advanced undergraduate students and graduate students with prior knowledge of calculus and a college physics course. Introduction to how physical principles offer insights into modern biology, with regard to the structural, dynamical, and functional organization of biological systems. Topics include the roles of free energy, diffusion, electromotive forces, non-equilibrium dynamics, and information in fundamental biological processes.

Lecture/lab emphasizing analog and digital electronics for lab research. RC and diode circuits. Transistors. Feedback and operational amplifiers. Active filters and circuits. Pulsed circuits, voltage regulators, and power circuits. Precision circuits, low-noise measurement, and noise reduction techniques. Circuit simulation tools. Analog signal processing techniques and modulation/demodulation. Principles of synchronous detection and applications of lock-in amplifiers. Common laboratory measurements and techniques illustrated via topical applications. Prerequisites: undergraduate device and circuit exposure.

Lecture/lab emphasizing analog and digital electronics for lab research. Continuation of APPPHYS 207 with emphasis on applications of digital techniques. Combinatorial and synchronous digital circuits. Design using programmable logic. Analog/digital conversion. Microprocessors and real time programming, concepts and methods of digital signal processing techniques. Current lab interface protocols. Techniques commonly used for lab measurements. Development of student lab projects during the last three weeks. Prerequisites: undergraduate device and circuit exposure. Recommended: previous enrollment in APPPHYS 207.

Provides a fundamental understanding of x-ray scattering and diffraction. Combines pedagogy with modern experimental methods for obtaining atomic-scale structural information on synchrotron and free-electon laser-based facilities. Topics include Fourier transforms, reciprocal space; scattering in the first Born approximation, comparison of x-ray, neutron and electron interactions with matter, kinematic theory of diffraction; dynamical theory of diffraction from perfect crystals, crystal optics, diffuse scattering from imperfect crystals, inelastic x-ray scattering in time and space, x-ray photon correlation spectroscopy. Laboratory experiments at the Stanford Synchrotron Radiation Lightsource.

Theoretical analysis of dynamical processes: dynamical systems, stochastic processes, and spatiotemporal dynamics. Motivations and applications from biology and physics. Emphasis is on methods including qualitative approaches, asymptotics, and multiple scale analysis. Prerequisites: ordinary and partial differential equations, complex analysis, and probability or statistical physics.

Structure of quantum theory emphasizing states, measurements, and probabilistic modeling. Generalized quantum measurement theory; parallels between classical and quantum probability; conditional expectation in the Schrödinger and Heisenberg pictures; covariance with respect to symmetry groups; reference frames and super-selection rules. Classical versus quantum correlations; nonlocal aspects of quantum probability; axiomatic approaches to interpretation. Prerequisites: undergraduate quantum mechanics, linear algebra, and basic probability and statistics.

Review of the basics of quantum information. Quantum optics: photon counting, detection, and amplification. Quantum noise in parametric processes. Quantum sensing: standard quantum limits, squeezed light, and spin squeezing. Gaussian quantum information. Quantum theory of electric circuits, electromagnetic components, and nanomechanical devices. Integrated quantum systems: superconductivity and Josephson qubits, measurement-based quantum computing with photons, spin qubits, topological systems. Prerequisites: PHYSICS 130/131 and APPPHYS 203.

Recent years have witnessed the successful application of time-honored techniques from the statistical physics of disordered systems, like the replica method and the cavity method, to understanding modern advances in machine learning and computation. We will develop the foundations of these methods, starting with a crash course in statistical mechanics, and then progressing to the basic theory of spin glasses, associative memories, random matrices, and random landscapes. We will additionally learn how to apply this theory to problems in learning and computation, including high dimensional statistics and deep learning. Overall, this foundations course will prepare students to read the growing interdisciplinary literature spanning physics, learning and computation.

Laboratory and lectures. Advanced microscopy and imaging, emphasizing hands-on experience with state-of-the-art techniques. Students construct and operate working apparatus. Topics include microscope optics, Koehler illumination, contrast-generating mechanisms (bright/dark field, fluorescence, phase contrast, differential interference contrast), and resolution limits. Laboratory topics vary by year, but include single-molecule fluorescence, fluorescence resonance energy transfer, confocal microscopy, two-photon microscopy, microendoscopy, and optical trapping. Limited enrollment. Recommended: basic physics, basic cell biology, and consent of instructor.

The efficient transport of energy, mass, and momentum is essential to the normal function of living systems. Changes in these processes often result in pathological conditions. Transport phenomena are also critical to the design of instrumentation for medical applications and biotechnology. The course aims to introduce the integrated study of transport processes and their biological applications. It covers the fundamental driving forces for transport in biological systems and the biophysics across multiple length scales (molecules, cells, tissues, organs, whole organisms). Topics include chemical gradients, electrical interactions, fluid flow, mass transport. Pre-requisites: Calculus, MATLAB, basic fluid mechanics, heat transfer, solid mechanics.

The genomics revolution has fueled a renewed push to model evolutionary processes in quantitative terms. This course will provide an introduction to quantitative evolutionary modeling through the lens of statistical physics. Topics will range from the foundations of theoretical population genetics to experimental evolution of laboratory microbes. Course work will involve a mixture of pencil-and-paper math, writing basic computer simulations, and downloading and manipulating DNA sequence data from published datasets. This course is intended for upper level physics and math students with no biology background, as well as biology students who are comfortable with differential equations and probability.

Cooperative effects in solids. Topics include the origin of magnetism in solids, crystal electric field effects and anisotropy, exchange, phase transitions and long-range order, ferromagnetism, antiferromagnetism, metamagnetism, density waves and superconductivity. Emphasis is on archetypal materials. Prerequisite: PHYSICS 172 or MATSCI 209, or equivalent introductory condensed matter physics course.

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.

Introduction to the many-body aspects of crystalline solids. Second quantization of phonons, anharmonic effects, polaritons, and scattering theory. Second quantization of Fermi fields. Electrons in the Hartree-Fock and random phase approximation; electron screening and plasmons. Magnetic exchange interactions. Electron-phonon interaction in ionic/covalent semiconductors and metals; effective attractive electron-electron interactions, Cooper pairing, and BCS description of the superconducting state. Prerequisite: APPPHYS 272 or PHYSICS 172.

Phenomenology of superconductivity viewed as a macroscopic quantum phenomenon. Topics include the superconducting pair wave function, London and Ginzburg-Landau theories, the Josephson effect, type I type II superconductivity, and the response of superconductors to currents, magnetic fields, and RF electromagnetic radiation. Introduction to thermal fluctuation effects in superconductors and quantum superconductivity.

Introduction to the physics of quantum optics and atoms in the ultracold setting. Quantum gases and photons are employed in quantum simulation, sensing, and computation. Modern atomic physics and quantum optics will be covered, including laser cooling and trapping, ultracold collisions, optical lattices, ion traps, cavity QED, BEC and quantum degenerate Fermi gases, and quantum phase transitions in quantum gases and lattices. Prerequisites: Undergraduate quantum and statistical mechanics courses.

Intended for first-year graduate students who are interested in understanding the basic concepts of ultrafast quantum science to prepare for research in AMO physics, condensed matter physics, physical chemistry or quantum information science.The topics in this course are distinct from and complementary to AP 201 (Laser and X-ray Sources and Science) and AP 203 (AMO Physics and Quantum Optics). Topics for this course: - Atomic structure probed in the time domain: Wave packets and quantum entanglement.- Molecular structure probed in the time domain: Building up and then breaking down the Born-Oppenheimer picture.- Extended quantum systems probed in the time domain: Band structure, phonons, and ultrafast disturbances- Laser-matter interactions: From multi-photon absorption to tunnel-ionization. - X-ray-matter interactions: Excitation, ionization, and linear and nonlinear scattering.- Attosecond science: Impulsive excitation, Auger-Meitner decay, charge migration within molecules.- Extreme time-domain quantum physics: high-field environments, and matter tunneling from the quantum vacuum.

Introduction to Superconducting Circuits is a comprehensive course designed to introduce students to the foundational theories and practical aspects of superconducting circuits, a key component in quantum computing. The syllabus covers a wide array of topics, starting with fundamental concepts like superconductivity, the Josephson effect. Students will learn about various types of superconducting qubits, quantum logic gate protocols, and circuit quantum electrodynamics. In addition to learning the theory, students will learn numerical simulation, optimal control, and learn about the experimental hardware. Prerequisites: APPPHYS 203 and APPPHYS 228.

Special studies under the direction of a faculty member for which academic credit may properly be allowed. May include lab work or directed reading.

Curricular practical training in Applied Physics. Arranged by student with research adviser's approval. Summary of activities required.

Survey of advances in the theory of neural networks, mainly (but not solely) focused on results of relevance to theoretical neuroscience.Synthesizing a variety of recent advances that potentially constitute the outlines of a theory for understanding when a given neural network architecture will work well on various classes of modern recognition and classification tasks, both from a representational expressivity and a learning efficiency point of view. Discussion of results in the neurally-plausible approximation of back propagation, theory of spiking neural networks, the relationship between network and task dimensionality, and network state coarse-graining. Exploration of estimation theory for various typical methods of mapping neural network models to neuroscience data, surveying and analyzing recent approaches from both sensory and motor areas in a variety of species. Prerequisites: calculus, linear algebra, and basic probability theory, or consent of instructor.

Physical biology of dynamical and mechanical processes in cells. Emphasis is on qualitative understanding of biological functions through quantitative analysis and simple mathematical models. Sensory transduction, signaling, adaptation, switches, molecular motors, actin and microtubules, motility, and circadian clocks. Prerequisites: differential equations and introductory statistical mechanics.

May be repeated for credit.

Cryogenics; low signal measurements and noise analysis; data collection and analysis; examples of current experiments. Prerequisites: PHYSICS 170, PHYSICS 171, and PHYSICS 172, or equivalents.

This course covers advanced topics in x-ray scattering including: diffuse scattering from static and dynamic disorder such as from defects or phonons; inelastic methods such as x-ray Raman and Compton scattering for measuring electronic structure and elementary excitations; and inelastic scattering in the time and frequency domain. Course combines lectures on basic principles with a review of foundational and current literature. May be repeat for credit.

Physics of particle beams in linear and circular accelerators. Transverse and longitudinal beam dynamics, equilibrium emittances in electron storage rings, high-brightness electron sources, RF acceleration and emittance preservation, bunch compression and associated collective effects, accelerator physics design for x-ray FELs, advanced accelerator concepts.

Synchrotron radiation sources for scientific exploration, and x-ray FELs for studies of ultrafast processes at the atomic scale. Fundamental concepts in electron and photon beams, bending magnet and undulator radiation, one-dimensional and three-dimensional FEL theory and simulations, self-amplified spontaneous emission, seeding and other improvement schemes, x-ray methodology, techniques and instrumentation for the study of ultrafast phenomena. Includes selected laboratory tours of the Linac Coherent Light Source and/or Stanford Synchrotron Radiation Lightsource at SLAC. Prerequisite: graduate-level electrodynamics, or consent of instructor.

Gaussian and unit sphere quadrature, singular value decomposition and principal component analysis, Krylov methods, non-linear fitting and super-resolution, independent component analysis, 3d reconstruction, "shrink-wrap", hidden Markov methods, support vector machines, simulated annealing, molecular dynamics and parallel tempering, Markov state methods, Monte Carlo methods for constrained systems.

Reading and discussion of selected works of contemporary literature (fiction) and philosophy that engage concepts of modern physics grounded in relativity and quantum theory. This is intended as a seminar that mixes students from physical sciences and the arts/humanities, with no specific prerequisites-- we will discuss the physics invoked by works of fiction and philosophy in a conceptually rigorous but non-mathematical way. How do writers of speculative fiction make sense of challenging ontological claims from empirical science, what implications do they explore, and how is the worldview of theoretical physics augmented or contested?

This course will explore key literature regarding quantum simulation, the use of atoms and qubits to emulate complex quantum matter of relevance to condensed matter physics, high-energy physics, and quantum information processing. Advanced topics including optical lattice-based and ion-trap quantum simulation, synthetic gauge fields, low-dimensional systems, nonequilibrium quantum many-body physics, and many-body cavity QED will be addressed in a seminar format. Presentations and a final paper will be required. Prerequisites: Quantum mechanics at the advanced undergraduate or 1st-year graduate level. May be repeated for credit.

This course will develop the subject of Strong-Field QED. Topics to be covered include: The structure of the quantum vacuum;relativistic laser-vacuum interactions;linear and non-linear Compton and Breit-Wheeler pair-production processes;vacuum polarization and vacuum tunneling; the radiation reaction problem in strong fields;applications in astrophysics and cosmology. The course will also cover experimental methods, including petawatt lasers with focused intensities sufficient to destabilize the vacuum. Prerequisites: familiarity with quantum mechanics, electrodynamics, and special relativity.

Students explore the use of Stanford Nano Shared Facilities (SNSF) for physical analysis of material samples of interest for art conservation, technical art history and archaeology. Weekly SNSF demonstrations will be supplemented by lectures on intellectual context by Stanford faculty/staff and conservators from the Fine Arts Museums of San Francisco (FAMSF). Students will undertake analysis projects derived from ongoing conservation efforts at FAMSF, including training on the use of relevant SNSF instruments and data analysis.

Survey of methods used to relate RNA sequences to the structure and function of transcribed RNA molecules. Computation of contributions of the counter-ion cloud to the dependence of free energy on conformation of the folded RNA. The relation of structure to function of ribozymes, riboswitches, and the formation of ribosomal proteins.

Current research and literature; offered by faculty, students, and outside specialists. May be repeated for credit.

Current research topics in lasers, quantum electronics, optics, and photonics by faculty, students, and invited outside speakers. May be repeated for credit.

The course covers the fundamentals of beamforming and array processing as applied to medical ultrasound imaging. Topics of the course include the physics of wave propagation, sampling requirements for aperture data, beamforming in the time and frequency domains, noise in beamforming, and ultrasound data acquisition geometries. Students will learn how to analyze and implement different beamforming techniques through project-based assignments.

This course presents the application of rigorous image processing, computer vision, machine learning, computer graphics and artificial intelligence techniques to problems in the history and interpretation of fine art paintings, drawings, murals and other two-dimensional works, including abstract art. The course focuses on the aspects of these problems that are unlike those addressed widely elsewhere in computer image analysis applied to physics-constrained images in photographs, videos, and medical images, such as the analysis of brushstrokes and marks, medium, inferring artists¿ working methods, compositional principles, stylometry (quantification of style), the tracing of artistic influence, and art attribution and authentication. The course revisits classic problems, such as image-based object recognition, but in highly non-realistic, stylized artworks. Recommended: One of CS 131 or EE 168 or equivalent; ARTHIST 1B. Prerequisites: Programming proficiency in at least one of C, C++, Python, Matlab or Mathematica and tools/frameworks such as OpenCV or Matlab's Image Processing toolbox.

This course introduces deep learning methods and AI technologies applied to four main areas of Computer Graphics: rendering, geometry, animation, and imaging. We will study a wide range of problems on content creation for images, shapes, and animations, recently advanced by deep learning techniques. For each problem, we will understand its conventional solutions, study the state-of-the-art learning-based approaches, and critically evaluate their results as well as the impacts to researchers and practitioners in Computer Graphics. The topics include differentiable rendering/neural rendering, BRDF estimation, texture synthesis, denoising, procedural modeling, view synthesis, colorization, style transfer, motion synthesis, differentiable physics simulation, and reinforcement learning. Through programming projects and homework, students who successfully complete this course will be able to use neural rendering algorithms for image manipulation, apply neural procedural modeling for shape and scene synthesis, exploit data-driven methods for simulating physical phenomena, and implement policy learning algorithms for creating character animation. Recommended Prerequisites: CS148, CS231N

Emphasis is on applications in modern devices and systems. Topics include: Schr¿dinger's equation, eigenfunctions and eigenvalues, solutions of simple problems including quantum wells and tunneling, quantum harmonic oscillator, coherent states, operator approach to quantum mechanics, Dirac notation, angular momentum, hydrogen atom, calculation techniques including matrix diagonalization, perturbation theory, variational method, and time-dependent perturbation theory with applications to optical absorption, nonlinear optical coefficients, and Fermi's golden rule. Prerequisites: MATH 52 and 53, one of EE 65, ENGR 65, PHYSICS 71 (formerly PHYSICS 65), PHYSICS 70.

This course will present advanced topics in elastic effective medium theory, as applied to porous rocks.

Emphasis is on applications in modern devices and systems. Topics include: Schr¿dinger's equation, eigenfunctions and eigenvalues, solutions of simple problems including quantum wells and tunneling, quantum harmonic oscillator, coherent states, operator approach to quantum mechanics, Dirac notation, angular momentum, hydrogen atom, calculation techniques including matrix diagonalization, perturbation theory, variational method, and time-dependent perturbation theory with applications to optical absorption, nonlinear optical coefficients, and Fermi's golden rule. Prerequisites: MATH 52 and 53, one of EE 65, ENGR 65, PHYSICS 71 (formerly PHYSICS 65), PHYSICS 70.

This course provides students from technical backgrounds (e.g., physics, applied physics, electrical or chemical engineering, bioengineering, computer science, statistics) the opportunity to learn how they can apply their expertise to advancing experimental research in the neurosciences. Students will visit one neuroscience lab per week to watch experiments, understand the technical apparatus and animal models being used, discuss the questions being addressed, and interact with students and others conducting the research. This course is strongly encouraged for students who wish to apply to the NeuroTech graduate training program. Our course has limited enrollment, therefore, if you are interested in registering please complete the form here: https://forms.gle/QXmkVfCqeS4zHmwB7 prior and someone will follow-up with you with a permission code accordingly.

Applied Physics Core course appropriate for graduate students and advanced undergraduate students with prior knowledge of elementary quantum mechanics, electricity and magnetism, and special relativity. Interaction of electrons with intense electromagnetic fields from microwaves to x- ray, including electron accelerators, x-ray lasers and synchrotron light sources, attosecond laser-atom interactions, and x-ray matter interactions. Mechanisms of radiation, free-electron lasing, and advanced techniques for generating ultrashort brilliant pulses. Characterization of electronic properties of advanced materials, prospects for single-molecule structure determination using x-ray lasers, and imaging attosecond molecular dynamics.

How are the motions of objects and the behavior of fluids and gases determined by the laws of physics? Students learn to describe the motion of objects (kinematics) and understand why objects move as they do (dynamics). Emphasis on how Newton's three laws of motion are applied to solids, liquids, and gases to describe phenomena as diverse as spinning gymnasts, blood flow, and sound waves. Understanding many-particle systems requires connecting macroscopic properties (e.g., temperature and pressure) to microscopic dynamics (collisions of particles). Laws of thermodynamics provide understanding of real-world phenomena such as energy conversion and performance limits of heat engines. Everyday examples are analyzed using tools of algebra and trigonometry. Problem-solving skills are developed, including verifying that derived results satisfy criteria for correctness, such as dimensional consistency and expected behavior in limiting cases. Physical understanding fostered by peer interaction and demonstrations in lecture, and interactive group problem solving in discussion sections. Prerequisite: high school algebra and trigonometry; calculus not required.

Physics 41E (Physics 41 Extended) is a 5-unit version of Physics 41 (4 units) for students with little or no high school physics. Course topics and mathematical complexity are similar, but not identical to Physics 41. There is an additional class meeting every week, and attendance at all class sessions is mandatory. The extra classroom time and corresponding extra study time outside of class allows students to engage with concepts and become fluent in mathematical tools that include vector representations and operations, and relevant calculus. There is a strong emphasis on developing problem-solving skills, particularly as applied to real world examples, to leave students prepared for subsequent engineering, physics, or related courses they may take. The course will explore important physical principles in mechanics including: using Newton's Laws and torque to analyze static structures and forces; understanding the equations of kinematics; and utilizing energy in its many forms and applications. Prerequisites: Physics placement diagnostic AND Math 20 or higher. Corequisites: Completion of OR co-enrollment of Math 21 or higher. Since high school math classes vary widely, it is recommended that you take at least one math class at Stanford before or concurrently with Physics 41. In addition, it is recommended that you take Math 51 or CME 100 before taking the next course in the Physics 40 series, Physics 43. Priority will be given to students who have had little physics background.

What is temperature? How do the elementary processes of mechanics, which are intrinsically reversible, result in phenomena that are clearly irreversible when applied to a very large number of particles, the ultimate example being life? In thermodynamics, students discover that the approach of classical mechanics is not sufficient to deal with the extremely large number of particles present in a macroscopic amount of gas. The paradigm of thermodynamics leads to a deeper understanding of real-world phenomena such as energy conversion and the performance limits of thermal engines. In optics, students see how a geometrical approach allows the design of optical systems based on reflection and refraction, while the wave nature of light leads to interference phenomena. The two approaches come together in understanding the diffraction limit of microscopes and telescopes. Discussions based on the language of mathematics, particularly calculus. Physical understanding fostered by peer interaction and demonstrations in lecture, and discussion sections based on interactive group problem solving. In order to register for this class students must EITHER have already taken an introductory Physics class (20, 40, or 60 sequence) or have taken the Physics Placement Diagnostic at https://physics.stanford.edu/academics/undergraduate-students/placement-diagnostic. Prerequisite: PHYSICS 41 or equivalent. MATH 21 or MATH 51 or CME 100 or equivalent.

(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.

Introductory laboratory electronics, intended for Physics and Engineering Physics majors but open to all students with science or engineering interests in analog circuits, instrumentation, and signal processing. The first part of the course is focused on hands-on exercises that build skills needed for measurements, including input/output impedance concepts, filters, amplifiers, sensors, and fundamentals of noise in physical systems. Lab exercises include DC circuits, RC and diode circuits, applications of operational amplifiers, optoelectronics, synchronous detection, and noise in measurements. The second portion of the class is an instrumentation design project, where essential instrumentation for a practical lab measurement is designed, constructed, and applied for an experiment. Example measurements can include temperature measurement in a cryostat, resistivity measurement of a superconducting material, measurement of the 2-D position of an optical beam, development of a high impedance ion probe and clamp for neuroscience, or other projects of personal interest. The course focuses on practical techniques and insight from the lab exercises, with the goal of preparing undergraduates for laboratory research. No formal electronics experience is required beyond exposure to concepts from introductory Physics or Engineering courses (Ohm's law, charge conservation, physics of capacitors and inductors, etc.). Students who have previously taken Physics 105 should not enroll in this course due to significant overlap. Recommended prerequisite: (Physics 43 and 44) OR (Physics 81 (formerly Physics 63) and 89L (formerly Physics 67), OR (Engineering 40A or 40M).

Fundamental concepts. Introduction to Hilbert spaces and Dirac's notation. Postulates applied to simple systems, including those with periodic structure. Symmetry operations and gauge transformation. The path integral formulation of quantum statistical mechanics. Problems related to measurement theory. The quantum theory of angular momenta and central potential problems. Prerequisite: PHYSICS 131 or equivalent.

The course covers the fundamentals of beamforming and array processing as applied to medical ultrasound imaging. Topics of the course include the physics of wave propagation, sampling requirements for aperture data, beamforming in the time and frequency domains, noise in beamforming, and ultrasound data acquisition geometries. Students will learn how to analyze and implement different beamforming techniques through project-based assignments.

This course provides students from technical backgrounds (e.g., physics, applied physics, electrical or chemical engineering, bioengineering, computer science, statistics) the opportunity to learn how they can apply their expertise to advancing experimental research in the neurosciences. Students will visit one neuroscience lab per week to watch experiments, understand the technical apparatus and animal models being used, discuss the questions being addressed, and interact with students and others conducting the research. This course is strongly encouraged for students who wish to apply to the NeuroTech graduate training program. Our course has limited enrollment, therefore, if you are interested in registering please complete the form here: https://forms.gle/QXmkVfCqeS4zHmwB7 prior and someone will follow-up with you with a permission code accordingly.

Mathematical techniques from statistical physics have been applied with increasing success on problems form combinatorics, computer science, machine learning. These methods are non-rigorous, but in several cases they were proved to yield correct predictions. This course provides a working knowledge of these methods for non-physicists. Specific topics: the Sherrington-Kirkpatrick model; sparse regression with random designs;