Homework11 - Physics 401 Homework#11 1 A spherical...

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Physics 401 - Homework #11 1) A spherical harmonic (three points) . Apply the definition of the spherical harmonics to calculate the explicit functional form for Y 3 1 (  The definition is given, for example, in Griffiths, equations 4.27, 4.28, and 4.32. 2) L x eigenstates . L x and L z do not have eigenstates in common, because their operators do not commute. However, we can find eigenstates of L x which are linear combinations of the eigenstates of L z . a) (three point) Determine an expression for the (L x ) operator in terms of the ladder operators (L + ) and (L - ) (L-plus and L-minus). b) (three points) Show that the following combinations of angular momentum states are eigenstates of L x , and identify their eigenvalues. Hint: use the form of the L x operator determined in part (a). 1 , 1 0 , 1 2 1 , 1 2 1 3 1 , 1 1 , 1 2 1 2 1 , 1 0 , 1 2 1 , 1 2 1 1 state Lx state Lx state Lx c) (three points) Suppose that a particle is in the eigenstate "Lx-state-2", defined in part (b), and we measure the z component of the angular momentum. What values
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