How can I confirm Lz=ħ,0,-ħ using operators and eigenfunctions?

[kenyanchemist]

Hi,
I have a question
Given the function
L_zY_i^lm(θ,ϕ) =mħY_i^lm(θ,ϕ)
What steps can I take to confirm that
L_z=ħ,0,-ħ

 

[drvrm]

I have a question
Given the function
LzYilm(θ,ϕ) =mħYilm(θ,ϕ)
What steps can I take to confirm that
Lz=ħ,0,-ħ

you are writing an eigen value equation for the z component of angular momentum operator called Lz
Ylm are spherical harmonics which are eigen functions of L^2 and Lz
if L=1 then m can take values +1, 0, -1 so the possible eigen values will be -h bar, 0, hbar

now you are asking what steps to confirm - then you can write the form of Lz and apply on spherical harmonics with l=1 and see what possible values comes out from eigen value equation.

 

[kenyanchemist]

Umm... how do I go about that?! Please understand am like super new on quantum mechanics
Please show me

 

[Jilang]

You need the operators..
http://farside.ph.utexas.edu/teaching/qmech/Quantum/node71.html
And the eigenfunctions
https://en.m.wikipedia.org/wiki/Table_of_spherical_harmonics

 

[kenyanchemist]

You need the operators..
http://farside.ph.utexas.edu/teaching/qmech/Quantum/node71.html
And the eigenfunctions
https://en.m.wikipedia.org/wiki/Table_of_spherical_harmonics

Got it... many thanks