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Unformatted text preview: the expectation value of L z ? d) Assume that we measure L z and the result of the measurement is~ . What is the state of the system after the measurement? Determine the product L x L y after the measurement. 3. And the nal problem (Total: 20 pts) a) Work out the following commutators: [ L z , p x ] = i ~ p y , [ L z , p y ] =i ~ p x , [ L z , p z ] = 0 , b) Use the results obtained in part a) to evaluate the commutator [ L z , p 2 ]. c) Use that [ L x , p 2 ] = [ L y , p 2 ] = [ L z , p 2 ] (you do not have to show these relations) and the result obtained in part b) to show that the Hamiltonian H = ( p 2 / 2 m ) + V commutes with L 2 and L z , provided that V = V ( r ) depends only on r ....
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 Fall '08
 STEVEPOLLOCK
 Physics

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