This course is designed for math and science students who are not majoring in physics but would like to learn the principles of quantum mechanics rigorously. For the most part, we will discuss the so-called two-level systems and collections of such systems. A two-level system has two basic states from which all other states may be constructed by linear combinations. We will begin with a review of linear algebra in two dimensions where the normalized vectors represent physical states and 2 x 2 matrices represent physical quantities and transformations. We will introduce the algebra of complex numbers as needed. Our prime examples will be an electron spin in an external field, and the various polarization states of the photon. Next we will consider a larger system that consists of several two-level subsystems. Though such a system is still very simple to describe, surprisingly, it exhibits nearly all the subtle and challenging features of the quantum theory. With the formalism developed, we will explore a range of foundational questions and applications such as uncertainty and measurement, entanglement, the EPR challenge and Bell’s theorem, the no-cloning theorem and teleportation. The work in the course comprises regular problem sets, two midterm exams and a final. Two meetings per week.

Requisite: MATH 111 or equivalent. Although the course will cover the necessary mathematics, some prior familiarity with vectors, matrices and basic linear algebra is useful. Fall semester. Professor Jagannathan.