Recent content by Tom_12

Oh yes, of course. Thank you.

Does this happen: <\hat{O_A}^2> = <\hat{A}^2>-2<\hat{A}><\hat{A}>+<\hat{A}>^2 <\hat{O_A}^2> = <\hat{A}^2>-2<\hat{A}>^2+<\hat{A}>^2 <\hat{O_A}^2> = (ΔA)^2 ...? I am not sure what happens when you take the expectation value of a term that is already an expectation value, does it...

Homework Statement consider operator defined as \hat{O_A} = \hat{A} -<\hat{A}> show that (ΔA)^2=<\hat{O_A}^2> Homework Equations (ΔA)^2=<\hat{A}^2>-<\hat{A}>^2 The Attempt at a Solution (ΔA)^2=<\hat{A}^2>-<\hat{A}>^2 = <\hat{A}^2> - (\hat{A} -\hat{O_A})^2 = <\hat{A}^2> -...

I see, thank you very much

Ok, I have no idea if what I'm doing is right, but would really appreciate some guidance here: \begin{align*} &= \hbar e^{-i\phi} \left(-\frac{\partial}{\partial\theta} + i\cot\theta\frac{\partial}{\partial\phi}\right) \hbar e^{+i\phi} \left(+\frac{\partial}{\partial\theta} +...

Homework Statement Using the operator identity: \hat{L}^2=\hat{L}_-\hat{L}_+ +\hat{L}_z^2 + \hbar\hat{L}_z show explicitly: \hat{L}^2 = -\hbar^2 \left[ \frac{1}{\sin^2\theta} \frac{\partial^2}{\partial\phi^2} + \frac{1}{\sin\theta} \frac{\partial}{\partial\theta}...