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Classical explanation of double slit polarization experiment

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I have a disagreement with a Quantum mechanical scientist about a double slit experiment with polarizers, which gives interference or not depending on "which path" knowledge of the photon. That is alright with me, but I can calculate the same results with classical wave formula. He does not agree with me, but also does not seem to be familiar working with classical waves calculations. Is there someone here who is? Who can check if my calculations and conclusions are right?

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