Homework SolutionQuantum Operators: Pr Y & Pr^2 Y

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Homework Statement



I'm given the expression for the operator Pr Y

Pr Y= -ih(bar) (1/r) d/dr (r Y)

I want to find Pr^2 Y so I have dotted Pr with Pr

I expect to get:

-h(bar)^2 (1/r) d/dr [ Y(Y + r dY/dr)]

but my notes have omitted the first Y in the above bracket and I can't see why.
 
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there's nothing wrong with the answer, the Y shouldn't be there. Pr^2 Y means operating Pr on Pr Y
 
so it is! thanks
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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