Solving Angular Momentum Homework: <L^2>,<(L^2)^2>, etc.

[stunner5000pt]

Homework Statement

For the non stationary state

\Psi = \frac{1}{\sqrt{2}} \left(Psi_{100}+\Psi_{110}\right) = \frac{1}{\sqrt{2}} \left(R_{10}Y_{00}e^{-iE_{10}t/\hbar}+R_{11} Y_{10}e^{-iE_{11}t/\hbar}

find &lt;L^2&gt;,&lt;(L^2)^2&gt;,&lt;L_{z}&gt;,&lt;L_{z}^2&gt;,\Delta L^2, \Delta L_{z}

Homework Equations

&lt;L^2&gt;=\hbar^2 l(l+1)
&lt;(L^2)^2&gt;=(\hbar^2 l(l+1))^2
&lt;L_{z}&gt;=\hbar m_{l}
&lt;L_{z}^2&gt;=(\hbar m_{l})^2
\Delta x = \sqrt{&lt;x^2&gt;-&lt;x&gt;^2}

The Attempt at a Solution

&lt;L^2&gt;=\frac{\hbar^2}{2} \left(0(0+1) + 1(1+1)\right)= \frac{3}{2} \hbar^2
the answer is supposed to be hbar^2 ... what am i doing wrong...

&lt;(L^2)^2&gt; = \frac{\hbar^4}{4} \left((0(0+1))^2+(1(1+1))^2\right) =\frac{5}{4} \hbar^2

&lt;L_{z}&gt; = \frac{\hbar}{2} (0+0) = 0

&lt;L_{z}^2} = \frac{hbar^2}{4} (0) = 0

are the values right... i fear that i am sorely mistaken about how to calculate the expectation values

any help would be greatly appreciated!

 

[Meir Achuz]

For your first answer, try 1*2=2, and 0*1=0.
Also 0*1=0 for the second answer.
Back to arithmetic 101.

 

[stunner5000pt]

For your first answer, try 1*2=2, and 0*1=0.
Also 0*1=0 for the second answer.
Back to arithmetic 101.

OOPS

stupid me