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Use the dual wave/particle nature of light to show that angular momentum is quantized in the scattered light leaving the cage.

I'm having trouble starting this problem up. I think I'll have to solve some version of Schrodinger's equation, but I'm not sure. I thought of using Bragg's law, nλ = 2dsinθ, where I would set d = a in this case and try to figure out the case where n = 1. Can I assume a is quantized and have a = 2πR/N? I'm kind of lost so any help starting this problem up would be of great help.