MathGroup Archive 2000

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Associated Legendre Definition


Preben Bohn wrote:

> P(n,m,x) = (1-x^2)^(m/2) d^m/dx^m (P(n,x))

It's just the problem that there are many different conventions around.
The associated Legendre Polynoms are defined up to a factor of modulus
1. That's clear if you think about them as eigenfunctions of the Casimir
operator of the rotation group SO(3) in quantum mechanics (orbital
angular momentum squared) and the 3-component of the angular momentum.

Y_l^m(theta,phi)=exp(i m phi) P_l^m(cos(theta))

l=0,1,2,... and for given l: m=-l,-l+1,...,l-1,l



-- 
Hendrik van Hees		Phone:  ++49 6159 71-2751
c/o GSI-Darmstadt SB3 3.183	Fax:    ++49 6159 71-2990
Planckstr. 1			mailto:h.vanhees at gsi.de
D-64291 Darmstadt		http://theory.gsi.de/~vanhees/index.html


  • Prev by Date: Re: Associated Legendre Definition
  • Next by Date: Change objetive function in Non-Linear Fit
  • Previous by thread: Re: Associated Legendre Definition
  • Next by thread: Re: Associated Legendre Definition