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hw8 - PHYS 507 Homework VIII(Fall'05 Assigned Wednesday Due...

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PHYS 507 Homework VIII (Fall ’05) Assigned: December 14, 2005, Wednesday. Due: December 21, 2005, Wednesday, at 5:00 pm. 1. Let ~ J = ~ J 1 + ~ J 2 be the total angular momentum of two independent systems. Suppose the quantum numbers for J 2 1 and J 2 2 are j 1 and j 2 respectively and we consider the states for which J 2 is quantized with quantum number j . In this case all of these three vectors ~ J 1 , ~ J 2 and ~ J have known magnitudes but has uncertain orientations. Despite the uncertainty in orientation, these three vectors form a triangle and we can talk about definite values of the angles in this triangle. Physically, we tend to interpret the maximum j value ( j = j 1 + j 2 ) as corresponding to states where the vectors ~ J 1 and ~ J 2 are more or less parallel to each other. Similarly, minimum j value ( j = | j 1 - j 2 | ) corresponds to states where these vectors are more or less anti-parallel to each other. (a) Consider the particular case j 1 = 2 and j 2 = 1. Compute the angle between ~ J 1 and ~ J 2 for each possible value of j .
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