- #1
TheBlueDot
- 16
- 2
Hello,
I'm trying to calculate the measurement of the orbital angular momentum of the state l=1 and m = -1. The operator for the angular momentum squared is
## L^2 = -\hbar (\frac{1}{sin\theta}(\frac{\partial}{\partial \theta}(sin\theta\frac{\partial}{\partial \theta})) +\frac{1}{sin\theta^2}\frac{\partial^2}{\partial\phi^2}) ##,
which expands to
## L^2 = -\hbar (\frac{1}{sin\theta}(\frac{\partial sin\theta}{\partial \theta}\frac{\partial}{\partial \theta}+sin\theta \frac{\partial^2}{\partial \theta^2}) +\frac{1}{sin\theta^2}\frac{\partial^2}{\partial\phi^2}) ##
When operate this on the wave function ##Y_{1,-1} = csin\theta e^{-i\phi}##, I got
##Y_{1,-1}*(\frac{cos^2\theta}{sin\theta} -\frac{sin^2\theta}{sin\theta}-\frac{1}{sin\theta})##,
which is zero. The answer should be ##2\hbar^2##.
If the cosine term is zero, then I'll get the right result.
Please help!
Thanks
I'm trying to calculate the measurement of the orbital angular momentum of the state l=1 and m = -1. The operator for the angular momentum squared is
## L^2 = -\hbar (\frac{1}{sin\theta}(\frac{\partial}{\partial \theta}(sin\theta\frac{\partial}{\partial \theta})) +\frac{1}{sin\theta^2}\frac{\partial^2}{\partial\phi^2}) ##,
which expands to
## L^2 = -\hbar (\frac{1}{sin\theta}(\frac{\partial sin\theta}{\partial \theta}\frac{\partial}{\partial \theta}+sin\theta \frac{\partial^2}{\partial \theta^2}) +\frac{1}{sin\theta^2}\frac{\partial^2}{\partial\phi^2}) ##
When operate this on the wave function ##Y_{1,-1} = csin\theta e^{-i\phi}##, I got
##Y_{1,-1}*(\frac{cos^2\theta}{sin\theta} -\frac{sin^2\theta}{sin\theta}-\frac{1}{sin\theta})##,
which is zero. The answer should be ##2\hbar^2##.
If the cosine term is zero, then I'll get the right result.
Please help!
Thanks