Density Matrix of Unpolarized Light

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The discussion centers on difficulties in solving specific problems related to the density matrix of unpolarized light. The user seeks guidance on how to approach problem 31.i and mentions challenges with problem 29.iii. It is noted that in a purely statistical mixture, the density matrix is characterized by probabilities on the diagonal and zeros elsewhere. The conversation highlights the importance of understanding the structure of the density matrix in relation to unpolarized light. Overall, the thread emphasizes the need for foundational knowledge in quantum mechanics to tackle these problems effectively.
annaphys
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Homework Statement
Attached 31.i and ii
Relevant Equations
Attached
I have unfortunately no attempt for 31.i. I don't know how to start the problem. 31.ii is attached. Can someone give me a tip on how to start 31.i? I also have troubles solving 29.iii. I have attached that as well.
 

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When you have a purely statistical mixture, the density matrix contains the probabilities of the different outcomes on the diagonal and zeros everywhere else.
 
(a) The polarisation pattern is elliptical with maximum (1,1) and minimum (-1,-1), and anticlockwise in direction. (b) I know the solution is a quarter-wave plate oriented π/4, and half-wave plate at π/16, but don't understand how to reach there. I've obtained the polarisation vector (cos π/8, isin π/8) so far. I can't find much online guidance or textbook material working through this topic, so I'd appreciate any help I can get. Also, if anyone could let me know where I can get more...

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