In summary, the conversation discusses the familiar field combination ##E+iB## and its application to classical radiation and scattering phenomena. It is noted that ##E+iB## is only half of Maxwell's equation, with the other half being taken up by its friend, ##E-iB##. This field combination also obeys a separate Schrödinger equation. The conversation ends with the realization that this is a rather interesting topic that straddles the classical and quantum realms.
  • #1
Paul Colby
Insights Author
Gold Member
1,511
454
Some weeks ago I happened across a post that caught my eye. Dale asked a question about the number of photons in an electromagnetic field. His question was answered in full but what caught my attention in the discussion was seeing a familiar friend; the rather odd field combination, ##E+iB## [1]. The impetus for Dale’s question centered on ##E+iB## obeying a Schrödinger equation, $$i\frac{d}{dt}(E+iB) = \nabla\times(E+iB).$$
My interest in this field combination is its application to classical radiation and scattering phenomena. First, we need to point out that ##E+iB## is really only half of Maxwell’s equation. The other half is taken up by its friend, ##E-iB## obeying a new and completely separate Schrödinger equation, $$i\frac{\partial}{\partial t}(E-iB) = -\nabla\times(E-iB).$$
What’s shown here is rather interesting...

Continue reading...
 
Last edited:
  • Like
  • Love
Likes Dale, jim mcnamara, PhDeezNutz and 2 others
Physics news on Phys.org
  • #2
Cool, I just saw this. I didn't know that E+iB has a classical application too! Or maybe this is kind of straddling the classical/quantum fence
 
  • Like
Likes Paul Colby

1. What is duality in computational electromagnetic problems?

Duality in computational electromagnetic problems refers to the concept of using both electric and magnetic fields to describe electromagnetic phenomena. It is based on Maxwell's equations, which state that electric fields and magnetic fields are interrelated and can be transformed into each other.

2. How is duality used in computational electromagnetic problems?

Duality is used in computational electromagnetic problems by solving for both electric and magnetic fields simultaneously. This allows for a more accurate and complete representation of the electromagnetic phenomenon being studied.

3. What are the advantages of using duality in computational electromagnetic problems?

Using duality in computational electromagnetic problems allows for a more comprehensive understanding of the electromagnetic phenomenon being studied. It also allows for more accurate and efficient simulations, as both electric and magnetic fields are taken into account.

4. Are there any limitations to using duality in computational electromagnetic problems?

One limitation of using duality in computational electromagnetic problems is that it is only applicable to linear, isotropic materials. It also requires a high level of computational power and resources to accurately solve for both electric and magnetic fields simultaneously.

5. How can I incorporate duality into my computational electromagnetic simulations?

To incorporate duality into your computational electromagnetic simulations, you will need to use a software or algorithm that is capable of solving for both electric and magnetic fields simultaneously. It is also important to have a thorough understanding of Maxwell's equations and how they relate to duality in electromagnetic problems.

Similar threads

  • Electromagnetism
Replies
1
Views
1K
  • Electromagnetism
Replies
3
Views
905
Replies
1
Views
849
Replies
3
Views
653
Replies
7
Views
597
  • Electromagnetism
Replies
1
Views
645
Replies
3
Views
745
Replies
2
Views
544
Replies
4
Views
1K
Replies
2
Views
902
Back
Top