1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Spherical Harmonics within QM

  1. May 25, 2007 #1
    1. The problem statement, all variables and given/known data
    The spherical harmonics [tex]Y^m_l[/tex] with l=1 are given by
    [tex]Y^{-1}_1 = \sqrt{\frac{3}{8\pi}}\frac{x-iy}{r}, Y^0_1 = \sqrt{\frac{3}{4\pi}}\frac{z}{r}, Y^1_1 = -\sqrt{\frac{3}{8\pi}}\frac{x+iy}{r}[/tex]

    and they are functions of [tex]L^2[/tex] and [tex]L_z[/tex] where L is the angular momentum.

    i) From these functions find a new set of three functions [tex]X^m_1[/tex] which are now eigenfunctions of [tex]L^2[/tex] and [tex]L_x[/tex].


    2. Relevant equations



    3. The attempt at a solution
    I'm not 100% sure about this question. Is it asking me to give the spherical harmonics in terms of [tex]\theta, \phi[/tex]? I think I can do that, but if thats not the question, could someone please explain to me what is being asked of me.

    Thanks

    Brewer
     
  2. jcsd
  3. May 25, 2007 #2
    i think it would be better if you wrote your spherical harmonics in spherical coords ..

    but in any case
    if [itex] X_{lm} [/itex] is an eignefunction of L^2 and Lz then
    [tex] \hat{L_{z}} X_{lm} = mX_{lm} [/tex]
    and
    [tex] \hat{L^2} X_{lm} = l(l+1) X_{lm} [/tex]
    and i think Xlm would b acquired by finding a superposition of the three given eigenfunctions.
     
  4. May 25, 2007 #3
    Thats what the question gives, cartesian coords.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Spherical Harmonics within QM
  1. Spherical Harmonics (Replies: 1)

  2. Spherical harmonics (Replies: 0)

  3. Spherical Harmonics (Replies: 3)

  4. Spherical Harmonics (Replies: 3)

Loading...