Spherical Harmonics in Maple and Mathcad?

[Jim Rathman]

I have written a Maple program for constructing 2D and 3D plots
to illustrate various features of the wave function for
hydrogen. Associated Laguerre and Legendre polynomials are
needed; in Maple, I define these functions as follows:

with(orthopoly,L);
with(orthopoly,P);
AssocLaguerre:=(k,n,x)->n!*diff(L(n,x),x$k);
if m=0 then
AssocLegendre:=(l,m,x)->P(l,x)
elif m>0 then
AssocLegendre:=(l,m,x)->-(1-x^2)^(m/2)*diff(P(l,x),x$m)
elif m<0 then
AssocLegendre:=(l,m,x)->(1-x^2)^((-m)/2)*diff(P(l,x),x$(-m))
fi;

A cohort of mine would like to use Mathcad for this, since
Maple is not available to most of his students. Mathcad does
not include spherical harmonics functions (which include
Laguerre and Legendre); however, I know that a Mathcad
Applications Package (Numerical Methods) is available and it
_does_ include spherical harmonics. I would greatly appreciate
if someone who has the Numerical Methods package could give me
more details about it, especially with regards to the spherical
harmonics. Thanks!

============================================================================

Jim F. Rathman
Chemical Engineering
Ohio State University
Columbus, OH
rat...@kcgl1.eng.ohio-state.edu

============================================================================

[Tim McLarnan]

In article <27n018$i...@charm.magnus.acs.ohio-state.edu> writes:
>
> I have written a Maple program for constructing 2D and 3D plots
> to illustrate various features of the wave function for

> hydrogen....

Pardon me for asking a related question:

I wonder if anyone has nice ways to visualize molecular orbitals in Maple. I'd
like to sell our chemists on Maple. If I could not only use Maple to solve for
the Hueckel MOs of some molecule, but also display those MOs either as 3D plots
of electron density or as little orbitals on each atom with proper signs and
sizes, I think I'd have some interested customers.

Has anybody done this?
--
Tim McLarnan t...@math.earlham.edu
Dept. of Mathematics, Earlham College, Richmond, IN 47374 USA