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Unformatted text preview: PHYS 507 Homework IV (Fall ’05) Assigned: October 24, 2005, Monday. Due: November 2, 2005, Wednesday, at 5:00 pm. 1. A material is called optically active when the polarization direction of linearly polarized photons rotates as they move inside the material. (This is mainly due to different refractive indices for left and right circular polarization.) In this and the next problem, we are going to investigate the time dependence of the polarization state of a single photon in such a medium. Suppose that the time-development operator between 0 and t is given as U ( t, 0) = • cosΩ t- sinΩ t sinΩ t cosΩ t ‚ . Remember: When U ( t, 0) is applied to the state at time 0, it gives the state at time t . (a) Show that U ( t, 0) is a unitary operator. (b) Compute U ( t 2 ,t 1 ) (i.e., the operator which is applied on state at t 1 and gives the state at t 2 ). Show that U ( t 2 ,t 1 ) depends only on the difference t 2- t 1 . (Remember: U ( t 2 , 0) = U ( t 2 ,t 1 ) U ( t 1 , 0).) (c) Using the Schr¨odinger equation for...
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