On Tue, Jul 27, 2010 at 4:34 PM, Aaron S. Meurer <[email protected]> wrote:
>
> On Jul 27, 2010, at 5:16 PM, Ondrej Certik wrote:
>
>> On Tue, Jul 27, 2010 at 11:12 AM, Brian Granger <[email protected]> wrote:
>>> Ondrej,
>>> I just looked through this and it looks great.  Very nice.  Once the base
>>> quantum stuff is done, we can integrate it with the hydrogen.py stuff, so
>>> that the following would work:
>>>>>> s = HState(n, l, m)
>>>>>> s
>>> |nlm>
>>>>>> represent(s, PositionBasis())
>>> ...your functions...
>>> Looks great though and I would merge this.
>>
>> I pushed it in.
>>
>> Awesome. Plus we also have spherical harmonics in sympy and so we can
>> represent the 3D solution to the hydrogen atom too. Great benchmark
>> for our 3D FEM solver.
>>
>> One thing is that I would like to also be able to operate with the
>> R_nl and Y_lm and Laguerre polys and so on, as symbols. So eventually,
>> we need classes like
>>
>> LaguerreL
>> SphericalHarmonics
>> HydrogenRadial
>>
>> or something, and they will have methods like
>> "integrate_three_harmonics" and
>> "apply_some_transformation_rule_to_laguerre_polys" etc. And of course
>> "get_xyz_representation", "get_theta_phi_representation" and so on.
>>
>>
>> Ondrej
>>
>
> For those of these special functions that are defined by differential 
> equations, I also think it would be great to add solvers to dsolve() that can 
> return them as solutions when presented with their defining differential 
> equation.

symbolically? That'd be slower, wouldn't it? But sure.

But for many other systems, you can obtain the function at least
numerically. But such solvers probably belong to another package.

Ondrej

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