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Unformatted text preview: Physics 828: Problem Set I Due Wednesday, January 16 at 11:59 PM Note: all problems are worth 10 points unless otherwise stated 1. (20 pts.) In class, I discussed the translation operator, and explained how it can be expressed in terms of the momentum operator p . In this problem, you will consider rotation operators, and show that they can be expressed in terms of components of the angular momentum operator L . Start with a wave function expressed in spherical coordinates as ( r, , ). We now consider a rotation about the z axis by an angle . Let R z ( ) be the operator which has the following effect on the wave function : R z ( ) ( r, , ) = ( r, , ) . (1) (a). By expressing ( r, , ) in a Taylor series about ( r, , ), show that ( r, , ) = exp parenleftBigg parenrightBigg ( r, , ) , (2) and hence that R z ( ) = exp parenleftBigg parenrightBigg . (3) Hence, show that...
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