Deriving the L+-L- Formula in Quantum Mechanics

[venusfly]

Hello, I have a quantum mechanics problem. Here is the problem statement. I must derive this formula,

L+-L- =-(h/2π)^2[d²/dθ²+cotθ d/dθ +cot²θ d²/dθ²+id/dφ]

from this formula,

L+-L-=±(h/2π)e^±(iθ)[d/dθ + i cotθ d/dφ]

I have no idea how to approach this problem. Can anyone give me a suggestion on how to begin the proof? Thanks.

 

[HallsofIvy]

Something is wrong here: L+-L- can't be equal to both! The first is clearly a second derivative. Is it supposed to be something like (L+-L-)²?

 

[venusfly]

Done

Sorry, wrote it wrong. Got the answer though. Thanks.