- #1

- 117

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- Homework Statement
- Consider an operator A such that it satisfies the following commutation relations-

##[L_+,A] = 0##

##[L_z,A] = \hbar A##

Using these, find ##L_z(AY_{ll})## and ##L^2(AY_{ll})## , where ##AY_{ll}## is an eigenfunction of ##L_z## and ##L^2##.

Also, deduce ##AY_{ll}##.

- Relevant Equations
- ##L_+ = L_x +iL_y##

##L_z(Y_{ll}) = l\hbar (Y_{ll})##

I've tried figuring out commutation relations between ##L_+## and various other operators and ##L^2## could've been A, but ##L_z, L^2## commute. Can someone help me out in figuring how to actually proceed from here?