How to Solve for L^2 and Lz in an Isotropic Harmonic Oscillator?

jay_jsh
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Homework Statement


Homework Equations


The Attempt at a Solution

 

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so far what I have done is attached.

I think I have part answer to the part one. now I need help in the part with L^2 and Lz.
 

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Thread 'Modeling a graph that shows age in relation to depth of an ice sample'

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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