GRADUATE COURSE OFFERING
			FALL '97

		M393C:  Quantum Mechanics 

Time: MWF 10-11
Room: RLM ????
Instructor:  Lorenzo Sadun (RLM 9.114, 471-7121)
Unique number: ?????

This course, on the foundations of quantum mechanics (QM) from a
mathematical perspective, is intended for (math) grad students who
wish to learn the basics of quantum mechanics, either as a stepping
stone to quantum field theory (and all the amazing things physicists
are teaching us about topology and algebraic geometry) or for its
intrinsic interest.  Very little previous exposure to physics is
assumed --- a freshman mechanics course should be enough --- but
you should have a solid grounding in linear algebra.  Familiarity with
infinite-dimensional spaces (e.g. from the applied math prelim course)
and familiarity with Lie Groups (in particular, $SU(2)$ and $SO(3)$)
are helpful but not essential.

There are two big differences between this course and a QM course
given by the physics department.  First, a physics course gives far
more emphasis to calculational techniques -- how do you estimate the
ionization energy of a Helium atom? -- while we will be more concerned
with the conceptual framework.  Second, a physics course assumes that
the students have a fair amount of physical intuition, and works hard
at developing the corresponding mathematical formalism.
Mathematicians, however, find this formalism quite easy -- leading
some to say that QM is nothing more than Schur's Lemma and the
spectral theorem!  However, relating this formalism to physical
reality is, for mathematicians, very difficult.  While a physics
course spends much effort developing the mathematical machinery, we
will spend much effort developing an intuition about what this
machinery means.

For example, a basic "paradox" is whether an electron is a particle or
a wave.  A physicist learns to accept that an electron has both
particle-like and wave-like properties, and slowly learns about wave
packets, Fourier transforms, etc, as a means of modeling this bizarre
fact.  A mathematician sees no paradox at all --- an electron's wave
function is just an element of the familiar Hilbert space $L^2(R^n)$.
But that resolution is useless if he can't then relate particle-like
and wave-like properties to an element of $L^2$.


Textbook: TBA  (possibly the Feynman lectures, volume 3, supplemented
by lecture notes)

Consent of Instructors: Not required