Newtonian, Lagrangian, and Hamiltonian classical mechanics. Special relativity with relativistic mechanics.
Lie groups are groups of continuous symmetries, generalizing the familiar notion of rotation groups; Lie algebras are their infinitesimal versions. Lie groups describe the symmetries of many physical henomena, combining algebra and geometry in beautiful ways. This course provides an introduction to the rich theory of Lie groups and Lie algebras, using explicit matrix groups to demonstrate concepts from differential geometry and abstract algebra. In particular, the properties of the orthogonal and unitary groups will be studied, along with several applications.
A project-driven laboratory experience in computational physics. Includes the use of basic mathematical and numerical techniques in computer calculations leading to solutions for typical physical problems. Topics to be covered will coordinate with the Paradigms in Physics course sequence.
An introduction to thermal and quantum physics in the context of contemporary challenges faced by our society, such as power generation, energy efficiency, and global warming.
Physicists and other physical scientists and engineers routinely use algebra and calculus, including vector calculus, in problem-solving. But the hard part of physics problem solving is often at the beginning and end of the problem, namely getting to an algebraic expression from a description of a physical situation in words or other representations, and interpreting an algebraic expression as a statement about what will happen in the real world. This course will use examples from electromagnetism involving scalar and vector fields in the three-dimensional world to explore a variety of problem-solving methods, including using information from experimental data, approximations, idealizations, and visualizations. The emphasis will be on how geometry can help.
An introduction to thermal and quantum physics in the context of contemporary challenges faced by our society, such as power generation, energy efficiency, and global warming.
Thermodynamics and canonical statistical mechanics.
Introduction to quantum mechanics through Stern-Gerlach spin measurements. Probability, eigenvalues, operators, measurement, state reduction, Dirac notation, matrix mechanics, time evolution. Quantum behavior of a one-dimensional well.
A project-driven laboratory experience in computational physics. Includes the use of basic mathematical and numerical techniques in computer calculations leading to solutions for typical physical problems. Topics to be covered will coordinate with the Paradigms in Physics course sequence.
A project-driven laboratory experience in computational physics. Includes the use of basic mathematical and numerical techniques in computer calculations leading to solutions for typical physical problems. Topics to be covered will coordinate with the Paradigms in Physics course sequence.
Introduction to quantum mechanics through Stern-Gerlach spin measurements. Probability, eigenvalues, operators, measurement, state reduction, Dirac notation, matrix mechanics, time evolution. Quantum behavior of a one-dimensional well.
Quantum waves in position and momentum space; Bloch waves in one-dimensional periodic systems, and the reciprocal lattice; coupled harmonic oscillators; phonons.
Introduction to quantum mechanics through Stern-Gerlach spin measurements. Probability, eigenvalues, operators, measurement, state reduction, Dirac notation, matrix mechanics, time evolution. Quantum behavior of a one-dimensional well.
An introduction to thermal and quantum physics in the context of contemporary challenges faced by our society, such as power generation, energy efficiency, and global warming.
Quantum waves in position and momentum space; Bloch waves in one-dimensional periodic systems, and the reciprocal lattice; coupled harmonic oscillators; phonons.
Introduction to quantum mechanics through Stern-Gerlach spin measurements. Probability, eigenvalues, operators, measurement, state reduction, Dirac notation, matrix mechanics, time evolution. Quantum behavior of a one-dimensional well.
Entropy and quantum mechanics; canonical Gibbs probability; ideal gas; thermal radiation; Einstein and Debye lattices; grand canonical Gibbs probability; ideal Fermi and Bose gases; chemical reactions and phase transformations.
An introduction to thermal and quantum physics in the context of contemporary challenges faced by our society, such as power generation, energy efficiency, and global warming.
Vectors, vector functions, and curves in two and three dimensions. Surfaces, partial derivatives, gradients, and directional derivatives. Multiple integrals in rectangular, polar, cylindrical, and spherical coordinates. Physical and geometric applications.
A project-driven laboratory experience in computational physics. Includes the use of basic mathematical and numerical techniques in computer calculations leading to solutions for typical physical problems. Topics to be covered will coordinate with the Paradigms in Physics course sequence.
A project-driven laboratory experience in computational physics. Includes the use of basic mathematical and numerical techniques in computer calculations leading to solutions for typical physical problems. Topics to be covered will coordinate with the Paradigms in Physics course sequence.
A project-driven laboratory experience in computational physics. Includes the use of basic mathematical and numerical techniques in computer calculations leading to solutions for typical physical problems. Topics to be covered will coordinate with the Paradigms in Physics course sequence.
Gravitational and electrostatic forces; angular momentum and spherical harmonics, separation of variables in classical and quantum mechanics, hydrogen atom.
An introduction to thermal and quantum physics in the context of contemporary challenges faced by our society, such as power generation, energy efficiency, and global warming.
Dynamics of mechanical and electrical oscillation using Fourier series and integrals; time and frequency representations for driven damped oscillators, resonance; one-dimensional waves in classical mechanics and electromagnetism; normal modes.
A project-driven laboratory experience in computational physics. Includes the use of basic mathematical and numerical techniques in computer calculations leading to solutions for typical physical problems. Topics to be covered will coordinate with the Paradigms in Physics course sequence.
This course will discuss the geometry of both Lie groups and Lie algebras, with an emphasis on the exceptional cases and their description in terms of the octonions. Lie groups are groups of continuous symmetries, generalizing the familiar notion of rotation groups; Lie algebras are their infinitesimal versions. Symmetry groups describe many physical phenomena, and Lie groups are widely used in physics, notably in the description of fundamental particles.
In the late 1800s, Killing and Cartan classified the simple Lie algebras into 4 infinite classical families and 5 exceptional cases. The classical Lie algebras correspond to matrix groups over the reals, the complexes, and Hamilton's quaternions. In the 1960s, a unified description of the exceptional Lie algebras was given by Freudenthal and Tits in terms of the octonions, the largest of the four division algebras.
The goal of this course is to describe the structure of the corresponding exceptional Lie groups, utilizing tools from both geometry and algebra. We will discuss the general structure of Lie algebras and Lie groups, the classification theorem, and the Freudenthal–Tits magic square of Lie algebras, culminating in a treatment of the largest of the exceptional Lie groups, $E_8$, in terms of the octonions.
A project-driven laboratory experience in computational physics. Includes the use of basic mathematical and numerical techniques in computer calculations leading to solutions for typical physical problems. Topics to be covered will coordinate with the Paradigms in Physics course sequence.
Theory of static electric, magnetic, and gravitational potentials and fields using the techniques of vector calculus in three dimensions.
Introduction to quantum mechanics through Stern-Gerlach spin measurements. Probability, eigenvalues, operators, measurement, state reduction, Dirac notation, matrix mechanics, time evolution. Quantum behavior of a one-dimensional well.
Theory of static electric, magnetic, and gravitational potentials and fields using the techniques of vector calculus in three dimensions.
Introduction to quantum mechanics through Stern-Gerlach spin measurements. Probability, eigenvalues, operators, measurement, state reduction, Dirac notation, matrix mechanics, time evolution. Quantum behavior of a one-dimensional well.