What Are the Possible Values of Ly After Measuring L^2 as 6(h bar)^2?

[J man]

Homework Statement

Suppose L^2 is measured for a system and the value 6(h bar)^2 is obtained. If Ly is measured immediately after, what possible values can result?

Homework Equations

(L^2)psi= (h bar)^2*l(l+1)psi
(Ly)psi= m(h bar)

The Attempt at a Solution

to begin, I know L^2 and Ly are compatible (I think that matters in this case)

Now, I know when L^2 is applied to a system, the eigenvalue is in the form of:
(h bar)^2*l(l+1)

so, since I know my measured value was 6(h bar)^2, I then solved for l and got 2.
this means that my m values range from -2 through 2.

then I assumed that by operating the Ly operator and observing the system, the possible values take on the values of m(h bar) where m ranges from -2 to 2. Is this correct?

 

[JesseC]

Yes that is perfectly correct. When you say 'compatible' you mean the L^2 and Ly operators commute.

Might be worth pointing out that m ranges from -2 to 2 in integer steps. Thus possible values of m are -2 -1 0 1 2. There are always 2l+1 possible values of m.