 #1
 93
 13
 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.