Hi,

I'm looking for a pov code helping me to create an animation simulating
the schrodinger's wave equation.

Can somebody help?

Thanks
Walid

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"Walid" <wha### [at] onlinefr> wrote:
> Hi,
>
> I'm looking for a pov code helping me to create an animation simulating
> the schrodinger's wave equation.
>

Please be more spesific.  You're practically requesting a pov-script
that would render a large part of the physical reality, ie. everything.
At least tell us whether you want to do it with or without radiosity.

;-)

--
jussi

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"jute" <nomail@nomail> wrote:
> "Walid" <wha### [at] onlinefr> wrote:
> > Hi,
> >
> > I'm looking for a pov code helping me to create an animation simulating
> > the schrodinger's wave equation.
> >
>
> Please be more spesific.  You're practically requesting a pov-script
> that would render a large part of the physical reality, ie. everything.
> At least tell us whether you want to do it with or without radiosity.
>
> ;-)
>
> --
> jussi

You're right, I didn't specify the request.
No radiosity is needed. In fact I'm looking for the numerical solution of
the two dimensional wave equation by defining the wave source and the
boundries conditions (like in the case of the double-slit experiment) and
how to implement it in a pov code.
I hope I specified better the request.

Thanks
Walid

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Wasn't it Walid who wrote:
>Hi,
>
>I'm looking for a pov code helping me to create an animation simulating
>the schrodinger's wave equation.

It you've got the equation of a solution, then you could make an
isosurface from it, or you could use your solution as the function for a
media density pattern 
(see http://www.econym.demon.co.uk/isotut/patterns.htm#density)

If you've only got a numerical method of obtaining a solution, you may
be better off solving it with an external tool or program, and creating
df3 density files (or, for 2d solutions, a height_field image) for POV
to read. POV isn't a particularly fast mathematical number crunching
system.

-- 
Mike Williams
Gentleman of Leisure

Post a reply to this message

Mike Williams <nos### [at] econymdemoncouk> wrote:
> Wasn't it Walid who wrote:
> >Hi,
> >
> >I'm looking for a pov code helping me to create an animation simulating
> >the schrodinger's wave equation.
>
> It you've got the equation of a solution, then you could make an
> isosurface from it, or you could use your solution as the function for a
> media density pattern
> (see http://www.econym.demon.co.uk/isotut/patterns.htm#density)
>
> If you've only got a numerical method of obtaining a solution, you may
> be better off solving it with an external tool or program, and creating
> df3 density files (or, for 2d solutions, a height_field image) for POV
> to read. POV isn't a particularly fast mathematical number crunching
> system.
>
> --
> Mike Williams
> Gentleman of Leisure

Hi,

Unfortunately, I don't have the solution and I really don't know how to
solve it. However, the idea of using the density pattern is quite
interesting. I still need the numerical method to find the solution.

Walid

Post a reply to this message

"Walid" <wha### [at] onlinefr> wrote:
> Hi,
>
> I'm looking for a pov code helping me to create an animation simulating
> the schrodinger's wave equation.

Is this something like what you want to do?

"QuantumWell displays a wave function in either a square well or a harmonic
oscillator potential, evolving under a small perturbation that leaves the
energy of the system unchanged, but is otherwise random. The contours are
for the squared magnitude of the wave, with phase indicated by colour.
"

http://gregegan.customer.netspace.net.au/APPLETS/07/07.html

Check out the whole site: it's brilliant!

Post a reply to this message

"PM 2Ring" <nomail@nomail> wrote:
> "Walid" <wha### [at] onlinefr> wrote:
> > Hi,
> >
> > I'm looking for a pov code helping me to create an animation simulating
> > the schrodinger's wave equation.
>
> Is this something like what you want to do?
>
> "QuantumWell displays a wave function in either a square well or a harmonic
> oscillator potential, evolving under a small perturbation that leaves the
> energy of the system unchanged, but is otherwise random. The contours are
> for the squared magnitude of the wave, with phase indicated by colour.
> "
>
> http://gregegan.customer.netspace.net.au/APPLETS/07/07.html
>
> Check out the whole site: it's brilliant!

Hi,

Thanks for the link.

While waiting for answers I pursued my research on the web and I fell
on a site which contains exactly the things I'm looking for:

http://panoramix.ift.uni.wroc.pl/~maq/eng/waves.php
http://panoramix.ift.uni.wroc.pl/~maq/eng/quantum.php

The programs are written by Maciej Matyka in C++ (not provided). However,
the executables are provided for download.

Is it possible to implement such simulations in povray?

Thanks again
Walid

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Walid nous apporta ses lumieres en ce 2005-08-24 06:03:
> "PM 2Ring" <nomail@nomail> wrote:
> 
>>"Walid" <wha### [at] onlinefr> wrote:
>>
>>>Hi,
>>>
>>>I'm looking for a pov code helping me to create an animation simulating
>>>the schrodinger's wave equation.
>>
>>Is this something like what you want to do?
>>
>>"QuantumWell displays a wave function in either a square well or a harmonic
>>oscillator potential, evolving under a small perturbation that leaves the
>>energy of the system unchanged, but is otherwise random. The contours are
>>for the squared magnitude of the wave, with phase indicated by colour.
>>"
>>
>>http://gregegan.customer.netspace.net.au/APPLETS/07/07.html
>>
>>Check out the whole site: it's brilliant!
> 
> 
> Hi,
> 
> Thanks for the link.
> 
> While waiting for answers I pursued my research on the web and I fell
> on a site which contains exactly the things I'm looking for:
> 
> http://panoramix.ift.uni.wroc.pl/~maq/eng/waves.php
> http://panoramix.ift.uni.wroc.pl/~maq/eng/quantum.php
> 
> The programs are written by Maciej Matyka in C++ (not provided). However,
> the executables are provided for download.
> 
> Is it possible to implement such simulations in povray?
> 
> Thanks again
> Walid
> 
> 
> 
Not obvious, but I think it may be done, or aproximated. A simple wave on aplane is
easy. 
Interference of two, or many, waves can also be done. It can get slow. BUT, you need
to get the 
equations right first. For the quantum part, it can get very tricky, long to parse,
long to render, 
and very memory intensive.
Don't ask me, my maths skils are to rusty, and probably insufisent, when aproching
that kind of stuff ;)

Alain

Post a reply to this message

Alain <ele### [at] netscapenet> wrote:
> Walid nous apporta ses lumieres en ce 2005-08-24 06:03:
> > "PM 2Ring" <nomail@nomail> wrote:
> >
> >>"Walid" <wha### [at] onlinefr> wrote:
> >>
> >>>Hi,
> >>>
> >>>I'm looking for a pov code helping me to create an animation simulating
> >>>the schrodinger's wave equation.
> >>
> >>Is this something like what you want to do?
> >>
> >>"QuantumWell displays a wave function in either a square well or a harmonic
> >>oscillator potential, evolving under a small perturbation that leaves the
> >>energy of the system unchanged, but is otherwise random. The contours are
> >>for the squared magnitude of the wave, with phase indicated by colour.
> >>"
> >>
> >>http://gregegan.customer.netspace.net.au/APPLETS/07/07.html
> >>
> >>Check out the whole site: it's brilliant!
> >
> >
> > Hi,
> >
> > Thanks for the link.
> >
> > While waiting for answers I pursued my research on the web and I fell
> > on a site which contains exactly the things I'm looking for:
> >
> > http://panoramix.ift.uni.wroc.pl/~maq/eng/waves.php
> > http://panoramix.ift.uni.wroc.pl/~maq/eng/quantum.php
> >
> > The programs are written by Maciej Matyka in C++ (not provided). However,
> > the executables are provided for download.
> >
> > Is it possible to implement such simulations in povray?
> >
> > Thanks again
> > Walid
> >
> >
> >
> Not obvious, but I think it may be done, or aproximated. A simple wave on aplane is
easy.
> Interference of two, or many, waves can also be done. It can get slow. BUT, you need
to get the
> equations right first. For the quantum part, it can get very tricky, long to parse,
long to render,
> and very memory intensive.
> Don't ask me, my maths skils are to rusty, and probably insufisent, when aproching
that kind of stuff ;)
>
> Alain

Hi,

Indeed it's a complicated thing to code in povray.
Thanks anway for your answers.

Walid

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> 
> Hi,
> 
> Indeed it's a complicated thing to code in povray.
> Thanks anway for your answers.
> 
> Walid
> 
> 
> 

The solution for a square well:

    +--------+
    |        |
  L1|        |
    |        |
    +--------+
        L2

the hamiltonian for an infinitely deep square well is
  H = -(ħ²/2m)(ð²/ðx² + ð²/ðy²) + V(x,y)
   where V(x,y)=inf. for x<0, x>L1 or y<0, y>L2
         V(x,y)=0    for 0 =< x >= L1 and 0 =< y >= L2

   the Schroedinger is therefor
   (ð²psi/ðx²)+(ð²psi/dy²)=-(2mE/ħ²)psi

   the solution for valid waves and energies is:
   psi[n1,n2](x,y) = (4/(L1*L2))^(1/2) * sin(n1*PI*x/L1) * sin(n2*PI*y/L2)

   E[n1,n2] = (ħ²/8)*(n1²/L1²+n2²/L2²)

   with quantum numbers n1=1,2,3,.... and n2=1,2,3,...

   hope you see the characters as I typed them in (UTF-8).

   ... dave

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