Learning Green's Functions: Best Resources & Books

[auditor]

Do anyone have a recommendation for a great resource to learn Green's functions from? Preferably a book with a generous amount of examples. I'm thinking something like a solid introduction to applied partial differential equations or the like. Ideally, there would be a lot of illustrations as well.

I know people speak warmly about "Partial Differential Equations for Scientists and Engineers" by Stanley J. Farlow (Dover), but it seems a little light on the Green's function side. Would it be better to learn this from an electrodynamics text? My ultimate interest in Green's functions is 1) to get a better understanding of mathematical modeling in general and 2) to better understand its application in QFT (in terms of propagators).

Anyone have some sound advice on where to look? Thanks!

 

[jsea-7]

Websites:

* http://mathworld.wolfram.com/GreensFunction.html
* http://www.boulder.nist.gov/div853/greenfn/tutorial.html#review
* http://en.citizendium.org/wiki/Green's_function

Great Book: Green's Functions, Author G.F.Roach

Hope that helps a little bit :)

 

[auditor]

Thanks jsea-7. I was aware of the book by Roach, but fear it is a little verbose for my needs. Have you had a chance to study it closely?

 

[Peeter]

This one has many worked examples (and problems) in this area:

http://www.amazon.com/dp/048667164X/?tag=pfamazon01-20

It's a fairly cheap dover book, and is generally excellent in my opinion.

 

[auditor]

Thanks Peeter! I've been thinking of getting my hands on that one for a while now - perhaps I finally will. :) However, a quick look at the index doesn't seem too promising regarding Green's functions, but I might need better glasses... Do you have any particular passage in mind?

 

[Peeter]

chapter 7: Green's Functions.

 

[auditor]

Yup, books.google.com seems to be the right tool to evaluate Dover classics before purchase. :)

 

[Super Nade]

It depends on what aspect you wish to pursue? I learned it from a Vector-Space/Field perspective. The gist being, G(x,x') is a weighted sum of basis vectors. The calculus approach seems a bit un-intuitive.

 

[Bob_for_short]

... My ultimate interest in Green's functions is
1) to get a better understanding of mathematical modeling in general and
2) to better understand its application in QFT (in terms of propagators).

I have an introduction to Green's functions in Russian with very simple examples. I can translate some passages if you like. Maybe it is worth to add this chapter to the PF Library.

 

[auditor]

I have an introduction to Green's functions in Russian with very simple examples. I can translate some passages if you like. Maybe it is worth to add this chapter to the PF Library.

That would be great! As far as I understand, there are still some treasures unknown to the west in the scientific literature of the old Soviet union. I think it would be a great asset to the PF Library.

@Super nade: My familiarity with Green's functions is almost non-existing, so I'd like to learn both its computational side, as well as building up some mathematical intuition. From what sources did you learn the vector-space approach?

 

[Super Nade]

Auditor,

I was introduced to Green's functions when I took a class in Electrodynamics (Jackson) and it seemed very arbitrary back then.

It was re-introduced to me in the Group-Theory class I'm taking. I can safely say that I like the approach better. This is probably the best class I have taken in my life. We started off by saying "something exists" and "we can count" and proceeded to build up everything else from there.

I'd be happy to share my lecture notes (scanned pages/photocopies by post) with everybody here with the proviso that I get some help in typing it out electronically. I'd like an e-copy but my typing skills are rudimentary at best. :)

Syllabus:
1. Logic/What is Physics?
2. Basic Set theory
3. Groups
4. Fields
5. Vector Spaces
6. Operators as Matrices
7. Tensors
8. Orthonormal Functions and Gram Schmidt Orthogonalization
9. Legendre Polynomials
10. 1/r potential expansion
11. Spherical Harmonics
12. Green Functions
13. Brief intro to Complex Analysis.

There is a bit more that I missed out, but boy, am I glad I took this class or what!

 

[auditor]

@Super nade:

that seems like a really cool class. I'd be happy to type out a couple of pages. Have you checked out LyX? It's really convenient whenever you need to typeset anything with a certain amount of mathematics in it. Basically, it's a WYSIWYG-editor, which generates LaTeX-code. Make sure to check it out at http://www.lyx.org.

At the moment, everything is pretty crazy at work, so I can't promise much before xmas. Send me a private message, and I'll try to type out some. :)

 

[Pinu7]

I would be willing to type up a few chapters(also with LyX) if you need. I really like the Syllabus.

email: pikachun00b7@gmail.com

 

[Physicslad78]

Does anyone know how to derive the free Phonon Green function for monolayer Graphene or a book where it is derived in details...


Thank you

 

[bhavaji]

How does one obtain the propagator for a scalar field whose mass is not a constant,for example space-dependent? Could the Green's function be an option?Any refs.?