This physics course offers a sophisticated view of quantum mechanics and its proper mathematical foundation. In this first module of three you will review the basics of wave mechanics and be introduced to the variational principle. You will learn about the technology of spin one-half states and spin operators and get an in-depth look into linear algebra to establish the mathematical foundation necessary to do quantum mechanics. This course concludes by developing the bra-ket notation of Dirac. To follow this course you will need some basic familiarity with quantum mechanics. You must have seen the Schrödinger equation and studied its solutions for the square well potential, the harmonic oscillator, and the hydrogen atom. You must be proficient in calculus and have some knowledge of linear algebra. Completing the 3-part Mastering Quantum Mechanics series will give you the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics. Part 1: Wave Mechanics, Part 2: Quantum Dynamics Part 3: Entanglement, and Angular Momentum . The series will follow MIT’s on campus 8.05, the second semester of the three-course sequence on undergraduate quantum mechanics, and will be equally rigorous. 8.05 is a signature course in MIT's physics program and a keystone in the education of physics majors. Learner Testimonial “ I’ve thought long and hard to come up with a better MOOC than this one (I’ve completed 25 of these things over the past 2 years) and can’t do it. 8.05x is #1 and I suspect will stay that way for some time to come.” _ “Being an engineering student from India trying to shift to Physics, I am often faced with the requirement to study topics on my own. Very often this has led me to feel inadequate. 8.05x was the perfect opportunity for me to both gain knowledge and evaluate my understanding on a high quality international platform. It has really exceeded my expectations. Now, at the end of fifteen weeks, I feel more confident and hopefully I am more knowledgeable._”

Курс “Теория электромагнитного поля” посвящен изложению классической электродинамики. В основу положена специальная теория относительности Эйнштейна, в рамках которой электромагнитное поле описывается четырехмерным тензором в пространстве Минковского. Первая часть курса посвящена подробному изложению постулатов теории относительности и ее основных элементов, включая преобразования Лоренца, релятивистское сокращение длины, замедление времени, законы преобразования скоростей. Обсуждаются свойства энергии и импульса релятивистских частиц, упругие столкновения частиц и распады. Во второй части курса электромагнитное поле вводится как объект в пространстве Минковского, описываемый 4-вектором и 4-тензором. Выводятся уравнения движения заряженной частицы во внешнем поле и рассматриваются их свойства и простейшие решения. Обсуждаются свойства тензора электромагнитного поля, законы преобразования полей, инварианты поля. Построено выражение для действия системы, состоящей из заряженных частиц и электромагнитного поля. Получены уравнения Максвелла, закон сохранения заряда и закон сохранения энергии для системы заряженных частиц в электромагнитном поле. Третья часть курса содержит изложение электростатики и магнитостатики. Вводятся понятия дипольного и квадруполного моментов системы зарядов и магнитного момента системы токов. Подробно обсуждается разложение электрического и магнитного поля на больших расстояниях от системы зарядов и токов, а также поведение таких систем во внешнем слабо неоднородном поле. Четвертая часть курса посвящена описанию электромагнитных волн. Выводится волновое уравнение и строятся его простейшие решения в виде плоских волн. Сделаны оценки для силы светового давления. Обсуждается плоская монохроматическая электромагнитная волна, поляризация, волновой вектор и закон преобразования частоты волны при переходе между инерциальными системами отсчета (эффект Доплера). Пятая часть курса посвящена построению общего решения уравнений Максвелла для электромагнитных полей, создаваемых системой зарядов, совершающих заданное движение. Выводятся и обсуждаются выражения для запаздывающих потенциалов и потенциалов Лиенара–Вихерта. Подробно проанализировано выражение для электромагнитного поля точечного заряда, движущегося вдоль заданной траектории. В заключительной части курса излагается теория излучения электромагнитных волн. Рассмотрены дипольное, магнитно-дипольное и квадрупольное излучение, а также излучение быстро движущегося заряда. Получены общие выражения для спектров и приближенные асимптотические формулы для спектрально-углового распределения излучения ультрарелятивистских частиц. Рассмотрена задача о рассеянии электромагнитной волны системой нерелятивистских зарядов. Найдено поле в ближней зоне излучающей системы. Введено понятие силы радиационного трения и получена приближенная нерелятивистская формула для нее. Определяются приделы применимости классической электродинамики. Уровень и объем изложения в целом соответствуют содержанию II тома курса теоретической физики Л.Д. Ландау и Е.М. Лифшица. Лекции предназначены для студентов, специализирующихся в области экспериментальной и теоретической физики. Для освоения лекционного материала необходимо знание классической механики, дифференциального и интегрального исчисления и теории дифференциальных уравнений. Базовые сведения из векторного и тензорного анализа даются по мере изложения курса.

Preparing for the AP Physics 1 exam requires a deep understanding of many different topics in physics as well as an understanding of the AP exam and the types of questions it asks. This course is designed to teach you everything you need to know and help you prepare for the AP Physics 1 Exam. As you work through this course, you will find lecture videos taught by Rice professors, problem-solving sessions with expert AP Physics teachers, interactive lab experiences and practice questions. By the end of the course, you should be ready to take on the AP exam!

In this four-part series, we will explore AP Physics 1 concepts and prepare for the AP Physics 1 Exam in an exciting and entirely new way. Increase your skills – and your readiness – for the AP Exam though quality videos, inquiry labs, Hollywood-style Concept Trailers™, Direct Measurement Videos, AP problem-solving sessions and more! Part 1: Linear Motionincludes the College Board’s Science Practices and aligns with its new AP Curriculum Framework. You will learn how to use kinematics to describe translational motion, ways to apply the concepts of motion, force, mechanical energy, and momentum, and new strategies for solving motion problems. The enhanced AP Exam Prep +5 is bundled with the edX Verified Certificate. To get +5, register for the Verified Certificate. The course instructors will email you with directions for how to receive both the extra exam prep and certificate. You can view or download the complete College Physics for AP®Courses textbook by going to the Reading Assignments page in this course *Advanced Placement® and AP® are trademarks registered and/or owned by the College Board, which was not involved in the production of, and does not endorse, these offerings. Additional Courses in the Preparing for the APPhysics 1 Exam Sequence Preparing for the AP* Physics 1 Exam - Part 2: Rotational Motion Preparing for the AP* Physics 1 Exam - Part 3: Electricity & Waves Preparing for the AP* Physics 1 Exam - Part 4: Exam Prep

Super-Earths And Life is a course about life on Earth, alien life, how we search for life outside of Earth, and what this teaches us about our place in the universe. In the past decade astronomers have made incredible advances in the discovery of planets outside our solar system. Thirty years ago, we knew only of the planets in our own solar system. Now we know of thousands circling nearby stars. Meanwhile, biologists have gained a strong understanding of how life evolved on our own planet, all the way back to the earliest cells. We can describe how simple molecules can assemble themselves into the building blocks of life, and how those building blocks might have become the cells that make up our bodies today. Super-Earths And Life is all about how these fields, astronomy and biology, together with geology, can help answer one of our most powerful and primal questions: are we alone in the universe? HarvardX requires individuals who enroll in its courses on edX to abide by the terms of the edX honor code: https://www.edx.org/edx-terms-service . HarvardX will take appropriate corrective action in response to violations of the edX honor code, which may include dismissal from the HarvardX course; revocation of any certificates received for the HarvardX course; or other remedies as circumstances warrant. No refunds will be issued in the case of corrective action for such violations. Enrollees who are taking HarvardX courses as part of another program will also be governed by the academic policies of those programs. HarvardX pursues the science of learning. By registering as an online learner in an HX course, you will also participate in research about learning. Read our research statement: http://harvardx.harvard.edu/research-statement to learn more. Harvard University and HarvardX are committed to maintaining a safe and healthy educational and work environment in which no member of the community is excluded from participation in, denied the benefits of, or subjected to discrimination or harassment in our program. All members of the HarvardX community are expected to abide by Harvard policies on nondiscrimination, including sexual harassment, and the edX Terms of Service. If you have any questions or concerns, please contact [email protected] and/or report your experience through the edX contact form: https://www.edx.org/contact-us .

Are you interested in investigating materials and their properties with unsurpassed accuracy and fidelity? Synchrotrons and XFELs (X-ray free-electron lasers) are considered to be Science’s premier microscopic tools. They're used in scientific disciplines as diverse as molecular biology, environmental science, cultural heritage, catalytical chemistry, and studies of the electronic properties of novel materials - to name but a few examples. This course provides valuable insights into this broad spectrum of scientific disciplines, from the generation of x-rays - via a description of the machines that produce intense x-ray sources - to modern experiments performed using these facilities.

Knowing the geometrical structure of the molecules around us is one of the most important and fundamental issues in the field of chemistry. This course introduces the two primary methods used to determine the geometrical structure of molecules: molecular spectroscopy and gas electron diffraction. In molecular spectroscopy, molecules are irradiated with light or electric waves to reveal rich information, including: Motions of electrons within a molecule (Week 1), Vibrational motions of the nuclei within a molecule (Week 2), and Rotational motions of a molecule (Week 3). In the gas electron diffraction method, molecules are irradiated with an accelerated electron beam. As the beam is scattered by the nuclei within the molecule, the scattered waves interfere with each other to generate a diffraction pattern. In week 4, we study the fundamental mechanism of electron scattering and how the resulting diffraction images reveal the geometrical structure of molecules. By the end of the course, you will be able to understand molecular vibration plays an important role in determining the geometrical structure of molecules and gain a fuller understanding of molecular structure from the information obtained by the two methodologies. FAQ Do I need to buy a textbook? No, you can learn the contents without any textbooks. However, if you hope to learn more on the subjects treated in this course, you are recommended to read the textbook introduced below: Kaoru Yamanouchi, “Quantum Mechanics of Molecular Structures,” Springer-Verlag, 2012.

This three-module sequence of courses covers advanced topics in quantum computation and quantum information, including quantum error correction code techniques; efficient quantum computation principles, including fault-tolerance; and quantum complexity theory and quantum information theory. Prior knowledge of quantum circuits and elementary quantum algorithms is assumed. These courses are the second part in a sequence of two quantum information science subjects at MIT. The three modules comprise: 8.371.1x : Quantum states, noise and error correction 8.371.2x : Efficient quantum computing - fault tolerance and complexity 8.371.3x: Advanced quantum algorithms and information theory This third 8.371.3x course module draws upon quantum complexity and quantum information theory, to cover in depth advanced quantum algorithms and communication protocols, including Hamiltonian simulation, the hidden subgroup problem, linear systems, and noisy quantum channels. A prior course (or strong background) in quantum mechanics is required. Knowledge of linear algebra is also strongly recommended, and other helpful math topics to know include probability and finite fields. This course has been authored by one or more members of the Faculty of the Massachusetts Institute of Technology. Its educational objectives, methods, assessments, and the selection and presentation of its content are solely the responsibility of MIT. For more information about MIT’s Quantum Curriculum, visit quantumcurriculum.mit.edu .

This is the fourth of a series of four modules that cover calculus-based mechanics. You will explore simple harmonic motion through springs and pendulums. This short course will culminate in the ability to use the Taylor Formula to approximate a variety of other situations as simple harmonic motion. The modules are based on material in MIT's Physics I, which is required for all MIT undergraduates, and is being offered as an XSeries on edX. Please visit the Introductory Mechanics XSeries Program Page to learn more and to enroll in all four modules. To understand the material in this course you should have taken Mechanics: Kinematics and Dynamics , Mechanics: Momentum and Energ y, and Mechanics: Rotational Dynamics .

From February 3 to May 28, 2020, we are offering Effective Field Theory in a Live Archive format. This means that the course features and materials will once again all be available, staff will engage with learners in the discussion forum, and there will be updates to the course content. ----------------- 8.EFTx is an online version of MIT's graduate Effective Field Theory course. The course follows the MIT on-campus class 8.851 as it was given by Professor Iain Stewart in the Fall of 2013, and includes his video lectures, resource material on various effective theories, and a series of problems to facilitate learning the material. Anyone can register for the online version of the course. When the course is being taught on campus, students at MIT or Harvard may also register for 8.851 for course credit. Effective field theory (EFT) provides a fundamental framework to describe physical systems with quantum field theory. In this course you will learn both how to construct EFTs and how to apply them in a variety of situations. We will cover the majority of the common tools that are used by different effective field theories. In particular: identifying degrees of freedom and symmetries, formulating power counting expansions (both dimensional and non-dimensional), field redefinitions, bottom-up and top-down effective theories, fine-tuned effective theories, matching and Wilson coefficients, reparameterization invariance, and various examples of advanced renormalization group techniques. Examples of effective theories we will cover are the Standard Model as an effective field theory, integrating out the massive W, Z, Higgs, and top, chiral perturbation theory, non-relativistic effective field theories including those with a large scattering length, static sources and Heavy Quark Effective Theory (HQET), and a theory for collider physics, the Soft-Collinear Effective Theory (SCET). Course Flow Since this is an advanced graduate physics course, you will find that self-motivation and interaction with others is essential to learning the material. The purpose of the online course is to set you up with a foundation, to teach you to speak the language of EFT, and to connect you with other students and researchers that are interested in learning or broadening their exposure to this subject. Each week you will complete automatically graded homework problems to test your understanding and to help you master the material. You are expected to discuss the homework with other people in the class, but your online responses must be done individually. To facilitate these interactions there will be a forum for student-to-student discussions, with threads to cover different topics, and moderators with experience in this field. Student learning and discussions will also be prompted by questions posed after each lecture topic. There will be no tests or final exam, but at the end of the course each student will give a 30-minute presentation on an EFT topic of their choosing. The subject of effective field theory is rich and diverse, and far broader than we will be able to cover in a single course. The presentations will create an opportunity for you to learn about additional subjects beyond those in lecture from your fellow students. To facilitate this learning opportunity, each student will be required to watch and grade five presentations from among their fellow students. Since this is a graduate course, we anticipate that learning the subject and having the 8.EFTx materials available as an online resource will be more valuable to most of you than obtaining a grade. Therefore anyone who registers for the course will be able to retain access to the course materials after the course has ended. Note that when the course is archival mode that the problems can be attempted and checked in the same manner as when the course was running.