How to Use Duality in Computational Electromagnetic Problems

[Paul Colby]

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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[Dale]

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