[Lesson 26] QED Prerequisites Scattering 3: The radial wave function of a free particle

In this lesson we explore the spherical Bessel, Neuman, and Hankel functions which are all critical to our understanding of scattering theory. We will just accept the standard solutions, and explore the properties of the functions, except for the most important property: their asymptotic form. That study will be deeper and we leave that for the next lesson.

Note that I am missing a factor of 1/2 and 1/2i on the slide at 50:16 when defining the Bessel and Neumann function in terms of Hankel functions.

The software I usually use to produce the lectures is:

[danielroddy]

I appreciate the approach of showing how to recognize, find and look up the proper equation types and solutions. I found this to be highly effective in engineering as well. When I was in school too much for us was based on using Maple, Matlab, Mathematica, or other tools for solution, rather than going to the tables and solutions in books. When it came to having to code the solutions or even work with them, going to the books or NIST became necessary. It is a whole different skillset. Thank you so much for this.

[jacquessmeets]

Oeps.... Seeing this video, I wonder what are th prerequisites of the QED prerequisites?

[mehmetalivat]

Could you advice book for QED

For the interested,
These specials functions bessel, legendre and laguerre dif equations could be learn very easly with quantum mechanics book by Zettili.