Quantum Theory and Analysis

John Baez

October 9, 2008

Here are some lecture notes for a course I occasionally teach at UCR:

John Baez, Quantum Theory and Analysis, 57 pages.

The high points of this course are:

The spectral theorem for unbounded self-adjoint operators.
Stone's theorem on strongly continuous 1-parameter unitary groups.
The Kato-Rellich theorem on perturbations of unbounded self-adjoint operators, with applications to Schrödinger operators.

I may accumulate solutions to homework problems as the years roll by. So far I just have one:

John Baez and Christopher Walker, Comparing operator topologies. Show that the powers of the right shift operator converge to zero weakly, but not strongly. Show that the powers of the left shift operator converge to zero strongly, but not in norm.

If you discover any errors in the course notes please email me, and I'll try to correct them. I'll keep a list of errors that haven't been fixed yet.

You can also download LaTeX files of the lecture notes, if for some bizarre reason you want them. However, the authors keep all rights to this work, except when stated otherwise.