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.
A link to an electronic version of Arfken and Weber.
The 2015 Special Functions presentation list.
Here's the Physics Today article by Michael Berry on Special Functions. Let me know if the link doesn't work for you.
Reading (3.9 MB pdf) on Sturm-Liouville theory from Arfken and Weber.
Reading on the Frobenious 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
Math Methods Poetry (pdf):
Last modified 21 April 2015