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Question: a photon moving in the z direction is in a...

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A photon moving in the z direction is in a state l = α IX) + β ly), where 1χ》 and I)) are the states with linear polarization along the z and y dlirection, respectively. 1. The photon passes first through a linear polarizer with the polarization axis oriented in the y direction, then one rotated by 45° in the a - y plane and finally a third one with the axis oriented in the direction. Calculate, in terms of α and β, the probablity that the photon will emerge from the third polarizer. 2. What would the probability be if the middle polarizer were absent? Explain the dif- ference. b) Consider the case where the coefficients in (a) have the specific values α- and Show that this photon is in an eigenstate of the J, operator (z-component of the angular momentum). What is the eigenvalue? Hint: Try doing a rotation of the state by some angle ф around z, first by rotating explicitly the |at) and l) components and then by using the rotation operator and compare the two results. Recall that J is the generator of rotations.
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