# Courses tagged with "Calculus I" (279)

This course covers cosmology – the study of our entire universe. Where did the universe come from? How will it end? What is the nature of space and time? For the first time in human history, we can give precise, reliable answers to many cosmological questions, thanks to a spectacular series of recent breakthroughs. But many of the most fundamental mysteries remain unsolved. In this course we will cover the latest advances and the unsolved mysteries. We will explain the recent observations, and with the help of guest speakers Lawrence Krauss and Brian Cox, we will explore the theories behind modern cosmology.

This course is designed for people who would like to get a deeper understanding of astronomy than that offered by popular science articles and shows. You will need reasonable high-school level Maths and Physics to get the most out of this course.

This is one of four ANUx courses which together make up the Australian National University's first year astrophysics program. You can take these four courses in any order. These courses compromise the Astrophysics XSeries. Learn more about the XSeries program and register for all the courses in the series today!

The discovery of exoplanets is one of the greatest revolutions in modern astrophysics. Twenty years ago, we had no idea whether any of the countless stars out there beyond our solar system had planets or not.

Today, things are totally different. Over 1,000 planetary systems have been discovered. The universe is teeming with planets. And what strange planets they are - hot Jupiter-like planets skimming the surfaces of their stars, cold and lonely free-floating planets far from any star, planets made of diamond, planets with rain made of glass, super-Earths and even planets orbiting neutron stars. In this course, we’ll bring you up-to-date with the latest research on exoplanets, and how this research has revolutionised our understanding of the formation of solar systems like our own.

This course is designed for people who would like to get a deeper understanding of these mysteries than that offered by popular science articles and shows. You will need reasonable high-school level mathematics and physics to get the most out of this course.

This is the second of four ANUx courses which together make up the Australian National University's first year astrophysics program. It follows on from the introductory course on the Greatest Unsolved Mysteries of the Universe, and is followed by courses on the violent universe and on cosmology. These courses compromise the Astrophysics XSeries. Learn more about the XSeries program and register for all the courses in the series today!

Interested in exploring the deadliest and most mysterious parts of our universe? Or, investigating black holes, which warp the very fabric of space-time around them?

We will look at what we know about these objects, and also at the many unsolved mysteries that surround them. We will also study white-dwarf stars and neutron stars, where the mind-bending laws of quantum mechanics collide with relativity. And, examine dwarf novae, classical novae, supernovae and even hypernovae: the most violent explosions in the cosmos.

This course is designed for people who would like to get a deeper understanding of astronomy than that offered by popular science articles and television shows.You will need reasonable high-school level Maths and Physics to get the most out of this course.

This is the third of four ANUx courses which together make up the Australian National University's first year astrophysics program. It follows on from a course on the Greatest Unsolved Mysteries of the Universe, and a course on exoplanets. It is not necessary to have done the previous courses first: all necessary background material is repeated here. It is followed by a course on cosmology. These courses compromise the Astrophysics XSeries. Learn more about the XSeries program and register for all the courses in the series today!

This is the first of a two-semester subject sequence that provides the foundations for contemporary research in selected areas of atomic and optical physics. Topics covered include the interaction of radiation with atoms: resonance; absorption, stimulated and spontaneous emission; methods of resonance, dressed atom formalism, masers and lasers, cavity quantum electrodynamics; structure of simple atoms, behavior in very strong fields; fundamental tests: time reversal, parity violations, Bell's inequalities; and experimental methods.

This is the second of five modules to introduce concepts and current frontiers of atomic physics and to prepare you for cutting-edge research:

8.421.2x: Atomic structure and atoms in external field

8.421.3x: Atom-Light Interactions 1 -- Matrix elements and quantized field

8.421.4x: Atom-Light interactions 2 -- Line broadening and two-photon transitions

The second module, 8.421.2x, describes atomic structure, including electronic levels, fine structure, hyperfine structure and Lamb shift. You will then learn about how electric and magnetic fields shift atomic levels. The discussion of time-dependent electric fields prepares you for the interactions of atoms with light and for the dressed atom picture.

At MIT, the content of the five modules makes the first of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

In these modules you will learn about the interaction of radiation with atoms: resonance; absorption, stimulated and spontaneous emission; methods of resonance, dressed atom formalism, masers and lasers, cavity quantum electrodynamics; structure of simple atoms, behavior in very strong fields; fundamental tests: time reversal, parity violations, Bell's inequalities; and experimental methods.

Completing the two-course sequence allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics.

### FAQ

Who can register for this course?

Unfortunately, learners from Iran, Cuba, Sudan and the Crimea region of Ukraine will not be able to register for this course at the present time. While edX has received a license from the U.S. Office of Foreign Assets Control (OFAC) to offer courses to learners from Iran and Sudan our license does not cover this course.

Separately, EdX has applied for a license to offer courses to learners in the Crimea region of Ukraine, but we are awaiting a determination from OFAC on that application. We are deeply sorry the U.S. government has determined that we have to block these learners, and we are working diligently to rectify this situation as soon as possible.

*Course image uses graphic by SVG by Indolences. Recoloring and ironing out some glitches done by Rainer Klute. [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons*

This is the last of five modules to introduce concepts and current frontiers of atomic physics and to prepare you for cutting-edge research:

8.421.2x: Atomic structure and atoms in external field

8.421.3x: Atom-Light Interactions 1 -- Matrix elements and quantized field

8.421.4x: Atom-Light interactions 2 -- Line broadening and two-photon transitions

8.421.5x: Coherence

This fifth module, 8.421.5x, looks at a central theme of atomic physics - coherence. This includes coherence of single atoms for two-level systems and three-level systems, and coherence between atoms, which can result in superradiant behavior.

At MIT, the content of the five modules makes the first of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

In these modules you will learn about the interaction of radiation with atoms: resonance; absorption, stimulated and spontaneous emission; methods of resonance, dressed atom formalism, masers and lasers, cavity quantum electrodynamics; structure of simple atoms, behavior in very strong fields; fundamental tests: time reversal, parity violations, Bell's inequalities; and experimental methods.

Completing the two-course sequence allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics.

### FAQ

Who can register for this course?

Unfortunately, learners from Iran, Cuba, Sudan and the Crimea region of Ukraine will not be able to register for this course at the present time. While edX has received a license from the U.S. Office of Foreign Assets Control (OFAC) to offer courses to learners from Iran and Sudan our license does not cover this course.

Separately, EdX has applied for a license to offer courses to learners in the Crimea region of Ukraine, but we are awaiting a determination from OFAC on that application. We are deeply sorry the U.S. government has determined that we have to block these learners, and we are working diligently to rectify this situation as soon as possible.

*Course image uses graphic by SVG by Indolences. Recoloring and ironing out some glitches done by Rainer Klute. [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons*

This is the second of a two-semester subject sequence beginning with Atomic and Optical Physics I (8.421) that provides the foundations for contemporary research in selected areas of atomic and optical physics. Topics covered include non-classical states of light–squeezed states; multi-photon processes, Raman scattering; coherence–level crossings, quantum beats, double resonance, superradiance; trapping and cooling-light forces, laser cooling, atom optics, spectroscopy of trapped atoms and ions; atomic interactions–classical collisions, quantum scattering theory, ultracold collisions; and experimental methods.

This is the first of five modules to introduce concepts and current frontiers of atomic physics, and to prepare you for cutting-edge research:

8.421.1x: Resonance

8.421.2x: Atomic structure and atoms in external field

8.421.3x: Atom-Light Interactions 1 -- Matrix elements and quantized field

8.421.4x: Atom-Light interactions 2 -- Line broadening and two-photon transitions

The first module, 8.421.1x, introduces resonance as an overarching theme of the course. You will deepen your understanding of the physics of resonance by examining systems using both classical and quantum techniques. Of special importance is the precession of a magnetic moments in time-dependent magnetic fields.

At MIT, the content of the five modules makes the first of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

In these modules you will learn about the interaction of radiation with atoms: resonance; absorption, stimulated and spontaneous emission; methods of resonance, dressed atom formalism, masers and lasers, cavity quantum electrodynamics; structure of simple atoms, behavior in very strong fields; fundamental tests: time reversal, parity violations, Bell's inequalities; and experimental methods.

Completing the five-course sequence allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics.

**FAQ**

Who can register for this course?

Unfortunately, learners from Iran, Cuba, Sudan and the Crimea region of Ukraine will not be able to register for this course at the present time. While edX has received a license from the U.S. Office of Foreign Assets Control (OFAC) to offer courses to learners from Iran and Sudan our license does not cover this course.

Separately, EdX has applied for a license to offer courses to learners in the Crimea region of Ukraine, but we are awaiting a determination from OFAC on that application. We are deeply sorry the U.S. government has determined that we have to block these learners, and we are working diligently to rectify this situation as soon as possible.

*Course image uses graphic by SVG by Indolences. Recoloring and ironing out some glitches done by Rainer Klute. [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons*

This is the third of five modules to introduce concepts and current frontiers of atomic physics and to prepare you for cutting-edge research:

8.421.2x: Atomic structure and atoms in external field

8.421.3x: Atom-Light Interactions 1 -- Matrix elements and quantized field

8.421.4x: Atom-Light interactions 2 -- Line broadening and two-photon transitions

The third module, 8.421.3x, covers how atoms interact with light. First, dipole and higher order couplings are introduced, and concrete examples for selection rules and matrix elements are given. After quantizing the electromagnetic field and introducing photons, the Jaynes-Cummings model and vacuum Rabi oscillations are presented. Coherent and incoherent time evolution are discussed, also in the framework of Einstein's A and B coefficients.

Completing the two-course sequence allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics.

### FAQ

Who can register for this course?

This is the fourth of five modules to introduce concepts and current frontiers of atomic physics and to prepare you for cutting-edge research:

8.421.2x: Atomic structure and atoms in external field

8.421.3x: Atom-Light Interactions 1 -- Matrix elements and quantized field

8.421.4x: Atom-Light interactions 2 -- Line broadening and two-photon transitions

The fourth module, 8.421.4x, includes a comprehensive discussion of line broadening effects, including Doppler effect, sidebands for trapped particles, power broadening, and effects of interactions and collisions. The concept of two-photon transitions is relevant for Raman processes and light scattering.

### FAQ

Who can register for this course?

In this physics course, you will be introduced to the QED Hamiltonian (Quantum ElectroDynamics), and learn how to construct diagrams for light-atom interactions. Using your new tools you will study Van der Waals and Casimir interactions, resonant scattering and radiative corrections.

This course is a part of a series of courses to introduce concepts and current frontiers of atomic physics, and to prepare you for cutting-edge research:

- 8.422.1x: Quantum States and Dynamics of Photons
**8.422.2x: Atom-photon Interactions**- 8.422.3x: Optical Bloch Equations and Open System Dynamics
- 8.422.4x: Light Forces and Laser Cooling
- 8.422.5x: Ultracold Atoms and Ions for Many-body Physics and Quantum Information Science

At MIT, the content of the five courses makes the second of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

Completing the series allows you to pursue advanced study and research in cold atoms, as well as in specialized topics in condensed matter physics. In these five courses you will learn about the following topics:

- Quantum states and dynamics of photons
- Photon-atom interactions: basics and semiclassical approximations
- Open system dynamics
- Optical Bloch equations
- Applications and limits of the optical Bloch equations
- Dressed atoms
- Light force
- Laser cooling
- Cold atoms
- Evaporative cooling
- Bose-Einstein condensation
- Quantum algorithms and protocols
- Ion traps and magnetic traps

In this physics course, you will learn about the spontaneous and stimulated light force and friction force in molasses and optical standing waves. You will also study light forces in the dressed atom picture. The course will discuss the techniques of magneto-optical traps and sub-Doppler and sub-recoil cooling.

This course is a part of a series of courses to introduce concepts and current frontiers of atomic physics, and to prepare you for cutting-edge research:

- 8.422.1x: Quantum states and dynamics of photons
- 8.422.2x: Atom-photon interactions
- 8.422.3x: Optical Bloch equations and open system dynamics
**8.422.4x: Light forces and laser cooling**- 8.422.5x: Ultracold atoms and ions for many-body physics and quantum information science

At MIT, the content of the five courses makes the second of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

Completing the series allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics. In these five courses you will learn about the following topics:

- quantum states and dynamics of photons
- photon-atom interactions: basics and semiclassical approximations
- open system dynamics
- optical Bloch equations
- applications and limits of the optical Bloch equations
- dressed atoms
- light force
- laser cooling
- cold atoms
- evaporative cooling
- Bose-Einstein condensation
- quantum algorithms and protocols
- ion traps and magnetic traps

This physics course presents a general derivation of the master equation and the optical Bloch equations. You will learn about various solutions of the optical Bloch equations, and you will discuss the quantum Monte Carlo wavefunction approach. The course will conclude with a discussion of unraveling open system quantum dynamics.

This course is a part of a series of courses to introduce concepts and current frontiers of atomic physics, and to prepare you for cutting-edge research:

- 8.422.1x: Quantum states and dynamics of photons
- 8.422.2x: Atom-photon interactions
**8.422.3x: Optical Bloch equations and open system dynamics**- 8.422.4x: Light forces and laser cooling
- 8.422.5x: Ultracold atoms and ions for many-body physics and quantum information science

At MIT, the content of the five courses makes the second of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

Completing the series allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics. In these five courses you will learn about the following topics:

- quantum states and dynamics of photons
- photon-atom interactions: basics and semiclassical approximations
- open system dynamics
- optical Bloch equations
- applications and limits of the optical Bloch equations
- dressed atoms
- light force
- laser cooling
- cold atoms
- evaporative cooling
- Bose-Einstein condensationquantum algorithms and protocols
- ion traps and magnetic traps.

In this physics course, you will learn about the quantum description of light with applications to squeezed states of light and teleportation as well as the non-classical states of light and single photons. You will learn how to do metrology with light. You will also learn about correlations with photons as well as atom correlation functions.

This course is a part of a series of courses to introduce fundamental concepts and current frontiers of atomic physics, and to prepare you for cutting-edge research:

**8.422.1x: Quantum States and Dynamics of Photons**- 8.422.2x: Atom-photon Interactions
- 8.422.3x: Optical Bloch Equations and Open System Dynamics
- 8.422.4x: Light Forces and Laser Cooling
- 8.422.5x: Ultracold Atoms and Ions for Many-body Physics and Quantum Information Science

At MIT, the content of these five courses makes up the second of a two-semester sequence (8.421 and 8.422) for graduate students interested in Atomic, Molecular, and Optical Physics. This sequence is required for Ph.D. students doing research in this field.

In these five courses you will learn about the following topics: quantum states and dynamics of photons, photon-atom interactions: basics and semiclassical approximations, open system dynamics, optical Bloch equations, applications and limits of the optical Bloch equations, dressed atoms, light force, laser cooling, cold atoms, evaporative cooling, Bose-Einstein condensation, quantum algorithms and protocols, ion traps and magnetic traps.

Completing this series allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics.

In this physics course you will learn about ultracold bosons and fermions, and you will hear from Prof. Ketterle about Bose-Einstein condensation (BEC). Prof. Ketterle was among the first to achive BEC in the lab and was awarded the Nobel prize in 2001 for his work along with Eric Cornell and Carl Wieman. You will also learn about weakly interacting Bose gases, as well as superfluid to Mott insulator transition, BEC-BCS crossover, trapped ions and quantum gates with ions.

- 8.422.1x: Quantum states and dynamics of photons
- 8.422.2x: Atom-photon interactions
- 8.422.3x: Optical Bloch equations and open system dynamics
- 8.422.4x: Light forces and laser cooling
**8.422.5x: Ultracold atoms and ions for many-body physics and quantum information science**

Completing the series allows you to pursue advanced study and research in cold atoms, as well as specialized topics in condensed matter physics. In these five courses you will learn about the following topics:

- quantum states and dynamics of photons
- photon-atom interactions: basics and semiclassical approximations
- open system dynamics
- optical Bloch equations
- applications and limits of the optical Bloch equations
- dressed atoms
- light force
- laser cooling
- cold atoms
- evaporative cooling
- Bose-Einstein condensation
- quantum algorithms and protocols
- ion traps and magnetic traps.

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