I have: [tex]Y_l^m= Ne^{im\varphi}P_l^m(cos\theta)[/tex] where(adsbygoogle = window.adsbygoogle || []).push({});

[tex]P_l^m(cos\theta)[/tex] is the associated legendre polynomials: [tex] P_l^m(cos\theta)=(-1)^m(sin\theta)^m(\frac{d^m}{d (cos\theta)^m})[/tex]

The problem is that i want to use this expression to apply on it the creation operator for the orbital angular momentum operator i. e to make this function with m = -l; [tex]Y_{-l}^l \rightarrow Y_{-l+1}^l[/tex]

When i attempt this, i get a very complicated set of derivatives etc, because i havent specified the "l".

Now, my question is: can i prove this for the general case or do i have to use a specific case, for example l = 1?

The creation operator is: [tex] L_+ = L_x + iL_y [/tex]

thanks!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Expression for Yl,-l again

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