Using Green's functions in electrostatics

[quasar_4]

Hi everyone.

I'm in my first semester of Jackson right now, and most of it's fine, but I'm having a hard time understanding the use of Green's functions as Jackson describes them in chapters 1-4. Does anyone know of another good physics reference that might be more clear? I have plenty of the math methods type books, but I'm specifically looking for more connection to physics and building the Green's function approach into my physics intuition.

If this post is too vague, I can pinpoint a couple of specific problems that have given me headaches.

Thanks,

quasar_4

 

[stevenb]

Hi everyone.

I'm in my first semester of Jackson right now, and most of it's fine, but I'm having a hard time understanding the use of Green's functions as Jackson describes them in chapters 1-4. Does anyone know of another good physics reference that might be more clear? I have plenty of the math methods type books, but I'm specifically looking for more connection to physics and building the Green's function approach into my physics intuition.

If this post is too vague, I can pinpoint a couple of specific problems that have given me headaches.

Thanks,

quasar_4

I've looked at a number of physics books that cover this and they all seem unintuitive to me. I'll offer (a possibly controversial) suggestion. You could try electrical engineering texts on system theory. Here the Green's function approach (at least a special case of it) is used extensively. The strange thing is that you rarely see the term "Green's Function" in these texts. Instead system impulse response is considered, but the formalism is the same.

I'm an electrical engineer that took many physics courses. As an undergrad, I remember studying the Green's function approach in a "Mathematical Methods of Physics" class. I was confused at first and then realized linear system theory used this extensively. Somehow, system theory is an easier context to make sense of the principles. I sometimes wonder if electrical engineers long ago banished the term "Green's function" for being too intimidating. (well you do see it at the grad level, but there you can't hide from the mathematicians and physicists)

The following text is a good book on the subject, but it's not the only one. In this book, chapters 1 and 2 would be enough to show just how intuitive, simple and powerful the Green's function method is. I don't recommend buying a brand new hard cover book for this purpose, but if you can find it used or in soft-cover, or better yet at the library, I would recommend it. The first edition might even be better for your purpose.

https://www.amazon.com/dp/0138147574/?tag=pfamazon01-20

 

[Meir Achuz]

Chapter 5 of Franklin's "Classical Electromagnetism" cover Green's functions in electrostatics from a physical viewpoint.

 

[quantum123]

I agree with Steven.
Engineering text sometimes teaching better physics than physics textbook.
I do not understand why anybody wants to read Jackson. It is more like a reference than a textbook. There are so many pedagocially better books than Jackson or another one (Goldstein, yaks).