- #1

Irishdoug

- 102

- 16

- Homework Statement
- Find the probability distributions of the orbital angular momentum variables ##L^{2}## and ##L_{z}## for the following orbital state functions:

- Relevant Equations
- ##\Psi(x) = f(r) sin(\theta) cos(\theta)##

##\Psi(x) = f(r) cos^{2}(\theta)##

Find the probability distributions of the orbital angular momentum variables ##L^{2}## and ##L_{z}## for the following orbital state functions:

##\Psi(x) = f(r) sin(\theta) cos(\theta)##

##\Psi(x) = f(r) cos^{2}(\theta)##I am aware that the prob. distribution of an observable is ##|<a_{n} | \Psi >|^{2}## were ##a_{n}## are the eigenstates.

I'm at a loss of how to even start the question however. I'm unsure as to how to find l and m to, for example, use the spherical harmonics. Can someone point me in the right direction? Thankyou.

##\Psi(x) = f(r) sin(\theta) cos(\theta)##

##\Psi(x) = f(r) cos^{2}(\theta)##I am aware that the prob. distribution of an observable is ##|<a_{n} | \Psi >|^{2}## were ##a_{n}## are the eigenstates.

I'm at a loss of how to even start the question however. I'm unsure as to how to find l and m to, for example, use the spherical harmonics. Can someone point me in the right direction? Thankyou.