Society of Physics Students

hbar@phys.columbia.edu

Columbia University in the City of New York

Summer 2008

Joshua Lui, a graduate student, has organized a series of mini-lectures for undergraduates during the summer. These lectures focus particularly on the mathematics of quantum mechanics, presented in a manner that should be accessible to undergraduates who have not yet taken the course. At the same time, the lectures emphasize a different viewpoint from Griffiths and should be interesting even to students with a more advanced background.

 May, 2008

Speaker: Joshua Lui

Talk Title: Group Theory and Quantum Mechanics

Abstract:

The first series of lectures will focus on the use of group theory in quantum mechanics, and will suggest that the origin of many characteristics of quantum mechanics lies in the observed necessity of complex numbers to describe these phenomena. Some topics include matrix Lie groups, matrix Lie algebras, representations of SO(3) and SU(2) and applications in physics. Lecture notes: lecture 1, lecture 2, spinor representation of SO(3), spinor representation of Lorentz group.

 4 June, 2008

Speaker: Claire Zukowski

Talk Title: Formalism and Quantum Mechanics

Abstract:

What does Griffiths mean when he claims that quantum mechanics "lives in Hilbert space"? This informal presentation will give some motivation for introducing an infinite-dimensional setting in the physics, then examine some mathematical details leading to the choice of Hilbert space as this setting. The talk will also introduce some problems resulting from the application of Hilbert space theory to physics, including the sometimes faulty application of finite-dimensional theorems to infinite dimensional vector spaces, unbounded operators and the dirac delta function. Lecture notes can be found here. Comments and criticisms are welcome.