"Jellby" <jel### [at] M-yahoocom> wrote in message
news:3e217097@news.povray.org...
> Jaap Frank wrote:
>
> > the attached scene-files produce pictures of the
> > quantum wave functions of hydrogen.
> >
> > [...]
>
> Thanks, I see it's too complicated for a quick look, but I'll study it when
> I have a little more time. In case you're interested I attach my own
> version of hydrogen-like orbitals, I use a macro to define the orbital
> functions, and these functions can be used with media or isosurfaces.

I've had a quick look at your functions. I wiil study
them this week again, but the same thing applies for me:
time. I'm a teacher and tomorrow waits another school day.

> It seemed to work faster if I defined the functions and the normalization
> factors separately.

If you put them inside the functions, they are calculated everytime
the function is called, so because they are constants for a set of quantum
numbers, you better can declare them separately.

If you use my file you will be surpriced that the orientation of the orbitals
from my functions are different then from yours. That was a surprice
for me too, when I saw them the first time. I think that the following
has happened. Because atoms don't carry coordinate systems around,
the functions can be simplified by turning them along these axes.
I don't know if this is true, but I suspect this.

For the probability distribution you use:

  #declare f_Den = function(x,y,z) { pow(f_Orb(x,y,z),2) }

I've found in the book where I found my wave-functions
that it's better to multiply f_Den with 4*pi*R^2 for this is the surface
of the sphere where you look for your probability.
 ( R = sqrt(x*x+y*y+z*z), so you have to put it inside the declaration
   for the f_Den function)
I've seen pictures with and without this factor. It seems that it is not
a big deal, but the probability distributions are not totaly the same.

Then you do this:
  ......
  #declare Norm = n_Ang*n_Rad;
  #declare f_Orb = function(x,y,z) { f_Ang(x,y,z)*f_Rad(x,y,z) }
  #declare f_Den = function(x,y,z) { pow(f_Orb(x,y,z),2) }

  #declare Orb_pos = function(x,y,z) { value/Norm - f_Orb(x,y,z) }
  #declare Orb_neg = function(x,y,z) { value/Norm + f_Orb(x,y,z) }

  #declare Orb = function(x,y,z) { value/Norm - abs(f_Orb(x,y,z)) }
  #declare Den = function(x,y,z) { value/(Norm*Norm) - f_Den(x,y,z) }

It seems to me that you divide everything by Norm, but then your
dimensions are not correct anymore. You now have f_Orb(x,y,z) / Norm.
And why do you subtract the orbital from value?
Norm is part of the wave function and you use it separately.
I can't follow this. Can you explain?

[..]

> P.S. I neglected the 4*pi factor in the probability density.
See above.

> P.P.S. Can an isosurface be declared and then the function be altered?

The function that you use inside the isosurface have to be declared before,
else you get an error. But maybe you mean something else?

Regards,

Jaap Frank

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