A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Watch quantum "particles" tunnel through barriers. Explore the properties of the wave functions that describe these particles.

When do photons, electrons, and atoms behave like particles and when do they behave like waves? Watch waves spread out and interfere as they pass through a double slit, then get detected on a screen as tiny dots. Use quantum detectors to explore how measurements change the waves and the patterns they produce on the screen.

The electric field lines from a point charge evolve in time as the charge moves. Watch radiation propagate outward at the speed of light as you wiggle the charge. Stop a moving charge to see bremsstrahlung (braking) radiation. Explore the radiation patterns as the charge moves with sinusoidal, circular, or linear motion. You can move the charge any way you like, as long as you don���������t exceed the speed of light.

Broadcast radio waves from KPhET. Wiggle the transmitter electron manually or have it oscillate automatically. Display the field as a curve or vectors. The strip chart shows the electron positions at the transmitter and at the receiver.

Broadcast radio waves from KPhET. Wiggle the transmitter electron manually or have it oscillate automatically. Display the field as a curve or vectors. The strip chart shows the electron positions at the transmitter and at the receiver.

Learn about different types of radiometric dating, such as carbon dating. Understand how decay and half life work to enable radiometric dating to work. Play a game that tests your ability to match the percentage of the dating element that remains to the age of the object.

Learn about different types of radiometric dating, such as carbon dating. Understand how decay and half life work to enable radiometric dating to work. Play a game that tests your ability to match the percentage of the dating element that remains to the age of the object.

Laboratory or field work in earth, atmospheric, and planetary sciences. To be arranged with department faculty. Consult with department Education Office. This course introduces fundamentals of radon physics, geology, radiation biology; provides hands on experience of measurement of radon in MIT environments, and discusses current radon research in the fields of geology, environment, building and construction, medicine and health physics.

Explore forces, energy and work as you push household objects up and down a ramp. Lower and raise the ramp to see how the angle of inclination affects the parallel forces acting on the file cabinet. Graphs show forces, energy and work.

Explore forces, energy and work as you push household objects up and down a ramp. Lower and raise the ramp to see how the angle of inclination affects the parallel forces acting on the file cabinet. Graphs show forces, energy and work.

Explore forces and motion as you push household objects up and down a ramp. Lower and raise the ramp to see how the angle of inclination affects the parallel forces. Graphs show forces, energy and work.

In this hands-on activity rolling a ball down an incline and having it collide into a cup the concepts of mechanical energy, work and power, momentum, and friction are all demonstrated. During the activity, students take measurements and use equations that describe these energy of motion concepts to calculate unknown variables, and review the relationships between these concepts.

In this hands-on activity rolling a ball down an incline and having it collide into a cup the concepts of mechanical energy, work and power, momentum, and friction are all demonstrated. During the activity, students take measurements and use equations that describe these energy of motion concepts to calculate unknown variables and review the relationships between these concepts.

Discrete and continuum modeling of diffusion processes in physics, chemistry, and economics. Topics include central limit theorems, continuous-time random walks, Levy flights, correlations, extreme events, mixing, renormalization, and percolation.

Building upon their understanding of forces and Newton's laws of motion, students learn about the force of friction, specifically with respect to cars. They explore the friction between tires and the road to learn how it affects the movement of cars while driving. In an associated literacy activity, students explore the theme of conflict in literature, and the difference between internal and external conflict, and various types of conflicts. Stories are used to discuss methods of managing and resolving conflict and interpersonal friction.

There are several tutorials on the page for this link. This review is under the subheading "Momentum and Energy." It is a small group tutorial that leads students through the construction of an understanding of the concept of momentum and its conservation.

A three-semester subject sequence on quantum field theory stressing the relativistic quantum field theories relevant to the physics of the Standard Model. 8.323 is a one-semester self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics and condensed matter physics. Includes the basic tools of field theory required for phenomenological studies. Topics: Functional integral formulation of quantum mechanics and many-particle systems. Classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields. Feynman graphs, analytic properties of amplitudes and unitarity of the S-matrix. Renormalization and renormalization group. Spinors and the Dirac equation. Quantization of Dirac fields. Supersymmetry. Quantization of abelian gauge fields. Calculations in quantum electrodynamics. Classical Yang-Mills fields. The Higgs phenomenon and a description of the Standard Model. 8.324 is the second term of the quantum field theory sequence. Develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics: Quantization of nonabelian gauge theories. BRST symmetry. Perturbation theory anomalies. Renormalization and symmetry breaking. The renormalization group. Critical exponents and scalar field theory. Conformal field theory. 8.325 is the third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physic

8.323, Relativistic Quantum Field Theory I, is a one-term self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics.

Normally taken by physics majors in their sophomore year. Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; particle collisions. Relativity and electricity; Coulomb's law; magnetic fields. Brief introduction to Newtonian cosmology. Introduction to some concepts of General Relativity; principle of equivalence. The Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, Shapiro delay. This course, which concentrates on special relativity, is normally taken by physics majors in their sophomore year. Topics include Einstein's postulates, the Lorentz transformation, relativistic effects and paradoxes, and applications involving electromagnetism and particle physics. This course also provides a brief introduction to some concepts of general relativity, including the principle of equivalence, the Schwartzschild metric and black holes, and the FRW metric and cosmology.