How to Use Duality in Computational Electromagnetic Problems

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The discussion centers on the duality in electromagnetic fields, specifically the field combination ##E+iB##, which adheres to a Schrödinger equation. This combination is noted for its relevance in classical radiation and scattering phenomena, highlighting its role in understanding electromagnetic behavior. The counterpart, ##E-iB##, follows a separate Schrödinger equation, indicating a deeper relationship between these field representations. The conversation hints at the intriguing overlap between classical and quantum mechanics in this context. Overall, the exploration of these field combinations reveals significant insights into electromagnetic theory.
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...

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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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