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    My lecturer is so unhelpful.. I can only get a hold of 1 past paper solution for all the year's exams.. and I was just wondering if someone could help me with a few questions please?

    I'm stuck on the last part of question 1(c)
    and also 1(e)

    Please help! I'd be so grateful! Our lecturer for this topic kind of sucks.
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    bump?
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    I can have a look at this on Wednesday if you still need help then when I get back to the UK. This computer doesn't seem to be able to open PDF's :s
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    (Original post by TheRandomer)
    My lecturer is so unhelpful.. I can only get a hold of 1 past paper solution for all the year's exams.. and I was just wondering if someone could help me with a few questions please?

    I'm stuck on the last part of question 1(c)
    and also 1(e)

    Please help! I'd be so grateful! Our lecturer for this topic kind of sucks.
    Part 1C - use that

     \hat{H} = \dfrac{\hat{L}^2}{2I}

    to rewrite the commutation relations you're being asked to find in terms of L only. You can then use the commuation relations you found in the first part to find the commuation relations involving the hamiltonian without having to do loads of working out.

    e.g.

     \{ \hat{H},\hat{L_z} \} \equiv \dfrac{1}{2I} \{ \hat{L}^2,\hat{L_z} \}

    You can pull out the  \dfrac{1}{2I} term safely because it is a constant, not an operator.

    From memory I think that  \hat{L}^2 commutes with  \hat{L_z} so the answer to the first one is (I think) both can be known simultaneously with infinite precision.

    For part e, I think you need to do some algebraic manuipulation. You know that

     \{\hat{N},\hat{N}\} = \hat{N}\hat{N} + \hat{N}\hat{N} = 2\hat{N}^2

    So

     \hat{N}^2 = \dfrac{1}{2} \{\hat{N},\hat{N}\}

    You also know that

     \hat{b}\hat{b}^* + \hat{N} = \hat{I}  from the anticommutator you've given for bb*. I don't have time atm to work this out fully but I think this info should be enough to do the question?
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    Thanks! That's a great help, I'll give that rearranging type one a go in a sec. I was just wondering though, for part c when it gives a set of 3 operators and asks can they be measured simultaneously with inf precision.. how do I do this? Do I show that one of them commutes with the other two? Or can I do it all in one go..?

    (Original post by spread_logic_not_hate)
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    (Original post by TheRandomer)
    Thanks! That's a great help, I'll give that rearranging type one a go in a sec. I was just wondering though, for part c when it gives a set of 3 operators and asks can they be measured simultaneously with inf precision.. how do I do this? Do I show that one of them commutes with the other two? Or can I do it all in one go..?
    I think you have to do it like this:

     \{ \hat{H}, \hat{L_x}, \hat{L_z} \} = \{ \hat{H}, \hat{L_x} \hat{L_z} + \hat{L_z} \hat{L_x} \} = \{ \hat{H}, \hat{L_x} \hat{L_z} \} + \{ \hat{H}, \hat{L_z}\hat{L_x} \}

    i.e. stage by stage. There may be a quicker way though (using some anticommutation identity perhaps?) but I don't know it if there is!
 
 
 
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