- #1

CanIExplore

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## Homework Statement

Hey forum,

I copied the problem from a pdf file and uploaded the image:

http://img232.imageshack.us/img232/6345/problem4.png [Broken]

What is the probability that the measurement of L[tex]^{2}[/tex] will yield 2\hbar[tex]^{2}[/tex]

## Homework Equations

[tex]\left\langle L^{2} \right\rangle[/tex] = [tex]\left\langle \Psi \left| L^{2} \right| \Psi \right\rangle[/tex]

[tex] L^{2} \Psi \right\rangle[/tex] = [tex] \hbar^{2}l(l+1) \Psi \right\rangle[/tex]

## The Attempt at a Solution

So the problem I'm having is with part (b). I know how to calculate the expectation value of L[tex]^{2}[/tex]. But given a value of the expectation value, I have no idea how to calculate the probability that the expectation value will yield that given value.

Going back to the expectation value of x in a one dimensional potential, I remember that if I wanted to find the expectation value of the particle being outside, say a potential well located between the origin and x=a, my integral would be from a to infinity. but I don't see how to translate that to this case.

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