Cauchy-Riemann Theorem Example in Physics

  • #1
entropy2008
1
0
Homework Statement:
Are there any good examples of the Cauchy-Riemann theorem (for differentiability) in physics and how it's used?
Relevant Equations:
$$\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}$$
$$\frac{\partial u}{\partial y}=-\frac{\partial v}{\partial x}$$
I was thinking of the wavefunction in QM but I'm not sure how it's used and when.
 

Answers and Replies

  • #2
Ishika_96_sparkles
39
19
Please refer to the chapter on Conformal Mapping in any standard Complex analysis book (e.g. Churchill and Brown, Walter Rudin) or some engineering mathematics/Mathematical physics books (e.g. Kreyszig/ Arfken and Webber) and you would be able to find applications and problems related to two dimensional flows from the velocity potential and the stream functions defined by the vector functions u and v, respectively. Additionally, you could find examples related to the electrostatics and how it is used to solve otherwise difficult problems using regular real algebra and calculus (e.g. electric quadrupoles).

As far as QM is concerned, i am not sure if there is a sort of wave-function that conformal maps to another function in some transformed domain whose real and imaginary parts are related via the C-R equations.
 
  • Like
Likes TSny and entropy2008

Suggested for: Cauchy-Riemann Theorem Example in Physics

Replies
7
Views
816
Replies
5
Views
547
Replies
2
Views
507
Replies
0
Views
557
  • Last Post
Replies
1
Views
327
Replies
2
Views
407
Replies
11
Views
1K
Replies
0
Views
324
Replies
0
Views
359
Replies
2
Views
188
Top