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## Homework Statement

For the spherical solution of the Schrodinger equation in spherical coordinates given the superposition of spherical harmonic functions

[tex] \frac{1}{\sqrt{14}} (Y_{1,-1}+ 2Y_{1,0}+3Y_{1,1}) [/tex]

calculate [itex] <\hat{L_{z}}> [/itex] and [itex] \Delta L_{z} [/itex]

**2. The attempt at a solution**

now from my textbook (brehm and mullin)

[tex] <\hat{L_{z}}> = \hbar m_{l} [/tex]

[tex] <\hat{L_{z}}> = \frac{\hbar}{14} (-1 + 4(0) +9(1)) = \frac{8}{14} \hbar = \frac{4}{7} \hbar [/tex]

while [tex] <L_{z}^2> = (\hbar m_{l})^2 [/tex]

this implies that the uncertainty in the Z component of the angular momentum [itex] \Delta L_{z} =0 [/itex]

but i was marked wrong in my assignment for this...

am i missing something

is there a difference between [itex] <\hat{L_{z}}> [/itex] and [itex] <L_{z}> [/tex]?

thanks in advance for any input