# Resources and Course Material

### PHYSICS 6403

### MATHEMATICS 6802

We discuss basic mathematics indispensable for every student of physics.

The course is co-listed with mathematics 6802.

**Synopsis:** We discuss advanced mathematical methods absolutely indispensable for any research project in either experimental or theoretical physics. We start with complex variable theory and complex contour integration, with an emphasis on the indispensable practical knowledge regarding the application of these concepts “for serious physics research”. We continue with a discussion of coordinate transformations, based of course on matrix representations of the coordinate transformations, and basic vector analysis. Topics will include, among others things, Stokes’s theorem in both differential as well as integral form, and transformations into curvilinear coordinates, as well as Christoffel symbols and the different forms of gradient and divergence operators, in different coordinate systems (e.g., spherical and cylindrical). Tensors will be discussed. The separation ansatz for the solution of partial differential equations will be discussed and illustrated. A discussion of the most indispensable special functions necessary for physics research follows: orthogonal functions and solutions to ordinary differential equations, Gamma function, hypergeometric, confluent hypergeometric, Legendre, Laguerre, and Bessel functions, and Hermite polynomials. The course may end with a discussion of Green functions in one dimension, and possibly higher dimensions, or, interactively, with discussions on any topics where students feel the need for a refreshment of their mathematical background knowledge. The necessity of diligence, and the presence of pitfalls in the mathematical discussions, will be highlighted.

Here is the Syllabus for 6403.

Here is Exercise #1.

Here is Exercise #1X.

Here is an (evolving) scriptum (2022/01/26).

### PHYSICS 6111

The course PHYSICS 6111 treats electrodynamics (mostly electrostatics) on an advanced (graduate) level.

The emphasis is on mathematical methods which can be useful in a general context, for both theoretical as well as experimental physicists.

The course will be taught in the fall semester of 2021, in a revised version, with more emphasis on the mathematical background material, and on special functions useful for the treatment of large classes of physics problems. Multipole decompositions will also be a cornerstone of the approach taken in the fall semester of 2021.

Here is the Syllabus for Physics 6111.

Here is Exercise #1.

Here is Exercise #2.

Here is Exercise #2 (one typo corrected).

Here is Exercise #3. Here is Exercise #3X.

Here is Exercise #4.

Here is Exercise #5. Here is Exercise #5X. Here is Exercise #5 (with Heaviside Theta).

Here is Exercise #6.

Here is Exercise #7.

Here is Exercise #8.

Here is Exercise #9.

Here is Exercise #10.

Here is Exercise #11.

Here is Exercise #12.

Here is Exercise #13.

Office hourse: ANY TIME!!! (by appointment). Send an email to ulj@mst.edu.

Here is the scriptum (2021/12/02).

### PHYSICS 6211

The course PHYSICS 6211 treats graduate electrodynamics (radiation phenomena) with Green functions.

The syllabus can be **downloaded here**.

### Download: Radiating Dipole

The movie of the oscillating electric field for a radiating dipole can be found here [File will be provided]. (You may want to right-click the link and save the linked file to your hard drive.)

### Download: C Program for Lerch’s Transcendent

Provided is a C program that calculates Lerch’s transcendent of real arguments using convergence acceleration methods (nonlinear sequence transformations and the combined nonlinear-condensation transformation). After downloading the zipped tar file lerchphi.tar.gz, the individual files within the zipped tar file can be unbundled by executing the command “tar xvzf lerchphi.tar.gz”.

Download: lerchphi.tar.gz [File will be provided] (C program and documentation).

By Sergej V. Aksenov and Ulrich D. Jentschura. This is (still) version 1.00 of May 1, 2002.

### Download: Reference Data for Bethe Logarithms

In the sense of physics reference data, the values for all hydrogenic Bethe Logarithms with principal quantum numbers less than or equal to 200 con be downloaded here. See also the publication [U. D. Jentschura and P. J. Mohr, Phys. Rev. A 72, 012110 (2005)].