Relationship between angular momentum and spherical harmonics

  • #1
208
7
I'm having a hard time grasping the logical flow from orbital angular momentum to spherical harmonics. It feels like it's just sort of been sprung out of nowhere from both my lecture notes and the textbook. Can anyone help fill in the gaps that clearly must link them somehow?

How did I get from eigenvectors of L2 and Lz being functions that depend only on theta and psi to the spherical harmonics [tex]|lm>=Y^{m}_{l}(\theta,\phi)[/tex]?
 
Last edited:

Answers and Replies

  • #2
208
7
Digging around the internet has netted me that spherical harmonics are the normalized common eigenfunction of L2 and Lz.
 
  • #3
dextercioby
Science Advisor
Homework Helper
Insights Author
13,024
578
I beg your pardon ? Using the abstract Dirac formalism will get you the |lm> things. But don't forget that

[tex] Y^{m}_{l}(\theta,\phi) = \langle r,\theta,\phi|lm\rangle [/tex]

That is going from an abstract Hilbert space H to L2(R3,d3x) and then to spherical coordinates.
 
  • #4
208
7
How did I get from orbital angular momentum to spherical harmonics in the first place?
 
  • #5
dextercioby
Science Advisor
Homework Helper
Insights Author
13,024
578
The spherical harmonics are eigefunctions for the squared orbital angular momentum operator in the position representation.
 
  • #6
208
7
Got it, thanks!
 

Related Threads on Relationship between angular momentum and spherical harmonics

  • Last Post
Replies
1
Views
1K
Replies
3
Views
2K
Replies
6
Views
71K
Replies
1
Views
3K
Replies
1
Views
4K
Replies
22
Views
6K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
1
Views
2K
Top