PHYS 320: Mathematical Physics
In this course we will review, learn, and practice a number of mathematical tools which have practical use for physicists. The idea will be that these tools will be of use, not only in your remaining studies at Hamilton, but also in graduate school.
A "pedestrian guide'' to the mathematics, the course focus on the implementation of the methods and applications rather than proofs and placing the results in context within mathematics. So, even if you have had a course in one or more of the topics, the emphasis and even some of the methods will be new. I also hope that you will master much of the material so that you can easily use in research, further studies, or elsewhere in life.
The course is in lecture/discussion format punctuated by short presentations. I strongly encourage folks to ask questions and make observations. Much of the class time is spent making connections to physics. The course is somewhat unusual in that one first encounters new material in the reading and in a small number of problems. In class we focus on filling out understanding, answering questions, embellishing the material, and working through more examples.
Course information (pdf):
Questions, Problems and Reading (pdf):
Some recent topics:
The NIST Digital Library of Mathematical Functions.
Curious to see more on the energy discussion we started the semester with? I started with a article in Physics Today (July 2016).
Michael Berry's Physics Today article on Special Functions.
A video of standing waves on a soap film disk. The Bessel functions are identified. The background music may be safely ignored.
Reading (3.9 MB pdf) on Sturm-Liouville theory from Arfken and Weber.
Reading on the Frobenius method from Arfken. An example of the method starts on page 395.
The Bessel-y initial condition algebra for the "linearly lengthening pendulum".
What do 3D parabolic coordinates look like?
Reading on vector differentiation, particularly time dependent basis vectors (from Potter and Goldberg)
Dirac Notation Primer (There is also a little bit on the notation in Boas, see page 181.)
Lovely Simulations of hydrogenic orbitals from falstad.com
More on the 1938 Christmas discovery of Meitner and Frisch. Frisch visited his aunt who was in exile in Sweden.
The bare bones mathematica notebook on the double pendulum.
For more on spin networks you can dip into the spin network primer.
Math Methods Poetry (pdf):
Last modified 5 May 2017