Fall 2017

Quantum Mechanics of Two-Level Systems

Listed in: Physics and Astronomy, as PHYS-274


Jagu Jagannathan (Section 01)


A two-level quantum system is one whose states are represented by unit rays in a two-dimensional vector space.  Such a system is the simplest non-trivial quantum mechanical entity.  Nevertheless, a two-level system or a collection of such systems exhibits all of the challenging and subtle features for which the quantum theory is notorious.  Examples of two-level systems we will consider are the polarization states of a photon, the spin of an electron or similar particle, and any atomic system for which only two of its many energy levels are important in a given problem.  After an overview of the current state of quantum mechanics, we will spend about three weeks on a synopsis of the concepts of pre-quantum (classical) physics.  We will review complex numbers and matrix algebra mainly to establish a common notation. We then begin to explore quantum kinematics and dynamics of a two-level system in the language of matrices, as well as in the abstract language of vector spaces.  We extend the theory to a collection of two-level systems and discuss entanglement, the devil at the heart of quantum conundrums.   Discussions of the Uncertainty Principle, the Einstein-Podolsky-Rosen challenge, Schrodinger’s Cat, Bell’s theorem, the no-cloning theorem and quantum teleportation follow.  The work in the course consists of regular problem sets, two midterm tests, and a final short project presentation and report. No college physics is presupposed. Two meetings per week.

Requisites: MATH 211 and MATH 271/272.  Fall semester.  Professor Jagannathan.


Quantitative Reasoning


2022-23: Not offered
Other years: Offered in Fall 2015, Fall 2017