How to Use Duality in Computational Electromagnetic Problems

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SUMMARY

The discussion focuses on the application of the field combination ##E+iB## in computational electromagnetic problems, specifically its adherence to a Schrödinger equation, $$i\frac{d}{dt}(E+iB) = \nabla\times(E+iB)$$. This field combination is noted for its relevance in classical radiation and scattering phenomena, while its counterpart, ##E-iB##, follows a separate Schrödinger equation, $$i\frac{\partial}{\partial t}(E-iB) = -\nabla\times(E-iB)$$. The interplay between these two formulations highlights their significance in bridging classical and quantum physics.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with Schrödinger equations
  • Knowledge of classical radiation and scattering phenomena
  • Basic concepts of electromagnetic fields
NEXT STEPS
  • Research the implications of the field combination ##E+iB## in quantum mechanics
  • Explore the relationship between classical and quantum electromagnetic theories
  • Study the applications of Maxwell's equations in computational simulations
  • Investigate advanced topics in electromagnetic field theory
USEFUL FOR

Physicists, electrical engineers, and researchers in computational electromagnetics seeking to understand the duality of classical and quantum field theories.

Paul Colby
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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 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...
 
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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
 
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