In this quantum physics course you will learn the basics of quantum mechanics. We begin with de Broglie waves, the wavefunction, and its probability interpretation. We then introduce the Schrodinger equation, inner products, and Hermitian operators. We also study the time-evolution of wave-packets, Ehrenfest’s theorem, and uncertainty relations. Next we return to the Schrodinger equation, solving it for important classes of one-dimensional potentials. We study the associated energy eigenstates and bound states. The harmonic oscillator is solved using the differential equation as well as algebraically, using creation and annihilation operators. We discuss barrier penetration and the Ramsauer-Townsend effect. Finally, you will learn the basic concepts of scattering – phase-shifts, time delays, Levinson’s theorem, and resonances – in the simple context of one-dimensional problems. We then turn to the study of angular momentum and the motion of particles in three-dimensional central potentials. We learn about the radial equation and study the case of the hydrogen atom in detail. This course is based on MIT 8.04: Quantum Mechanics I. At MIT, 8.04 is the first of a three-course sequence in Quantum Mechanics, a cornerstone in the education of physics majors that prepares them for advanced and specialized studies in any field related to quantum physics. After completing 8.04x, you will be ready to tackle the Mastering Quantum Mechanics course on edX, which will be available in Spring 2021.

Global Warming Science teaches you about the risks and uncertainties of future climate change by examining the science behind the earth’s climate. You will be able to answer such questions as, “What is the Greenhouse Effect?” and “How and why has earth’s climate changed through geologic history?” This science course is designed for college sophomores and juniors with some preparation in college-level calculus and physics.

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._”

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 course we will demonstrate how a large-scale quantum processor could be built using these qubits. Among the topics that we will discuss are micro-architectures, compilers, and programming languages. The course will also cover some of the basics of quantum error-correction, an essential procedure that allows us to combat errors that arise during computations using delicate qubits. To complete the story arc from the hardware of quantum computers to their software, the course will discuss the main factors that triggered the efforts to build quantum computers in the first place: quantum algorithms. The course then concludes with a discussion on the quantum internet: what is it? How can it be built? Why is it useful? The course is a journey of discovery, so we encourage you to bring your own experiences, insights and thoughts via the forum! This course is authored by experts from the QuTech research center at Delft University of Technology. In the center, scientists and engineers work together to enhance research and development in quantum technology. QuTech Academy’s aim is to inspire, share and disseminate knowledge about the latest developments in quantum technology.

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 .