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**Unformatted text preview: **a) Calculate the frequency dependence of the reected X-ray on the scattering angle. Draw a rough plot. b) Why is it ok to treat the electrons as free? c) How would the result change if the electron were massless? d) If you didnt believe in quantized photon momenta, what kind of distribution would you have expected? (Stuck? Look at Comptons paper on the isite) 5. Coherent states of the Simple Harmonic Oscillator a) Calculate z ( e za ae za ) . b) Show that | z a = e za | a is an eigenstate of a . What is its eigenvalue? c) Calculate A n | z a ? d) Show that these coherent states are minimally dispersive: p q = 1 2 , where q 2 = A q 2 aA q a 2 and p 2 = A p 2 aA p a 2 , where A q a = a z | q | z A a z | z A and A p a = a z | p | z A a z | z A . e) Why cant you make an eigenstate of a ? 1...

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