GSoC Introduction. Perturbation theory

[weralwolf]

Hello, where my simple example of calculations corrections due to
perturbation theory for hole with infinite walls. I thinks I didn't
use all sympy features, so if it possible guide me.
Source: http://pygments.org/demo/16998/

P.S. Why my previous discussion("One more GSoC Introduction") was
deleted?

Regards,
Anatolii

[Alexey U. Gudchenko]

23.03.2011 19:57, weralwolf пишет:

> P.S. Why my previous discussion("One more GSoC Introduction") was
> deleted?
>
> Regards,
> Anatolii
>

Is it you're talk about?

http://groups.google.com/group/sympy/browse_thread/thread/3e6a1cf2c1cfd393?hl=en#

I found it in:

http://groups.google.com/group/sympy?hl=en
Click "View all" near "9 of 8344 messages"

--
Alexey U.

[Julien Rioux]

On Mar 23, 12:57 pm, weralwolf <weralw...@gmail.com> wrote:
> Hello, where my simple example of calculations corrections due to
> perturbation theory for hole with infinite walls. I thinks I didn't
> use all sympy features, so if it possible guide me.
> Source:http://pygments.org/demo/16998/

I think you forgot to put
from sympy import S

at the top.

Did I get it right that you calculate the ground state energy of the
1D infinite potential well of width $a$ with a perturbation which is
linear in $x$, up to second order in perturbation?

I think in general your code is fine. What you might want to do is
- have V an operator
- same for the unpertubed Hamiltonian H
- being able to write those operators in matrix form in a particular
basis
- find the basis which diagonalizes H
- use this basis to represent H and V in matrix forms
- compute perturbation theory to first, second, etc. order by looking
up the matrix forms
- make it general enough to handle degenerate cases

I think some of this is possible already, but I haven't looked deeply
into it.

[Jeron Smuta]

2011/3/23 Julien Rioux <julien...@gmail.com>

On Mar 23, 12:57 pm, weralwolf <weralw...@gmail.com> wrote:
> Hello, where my simple example of calculations corrections due to
> perturbation theory for hole with infinite walls. I thinks I didn't
> use all sympy features, so if it possible guide me.
> Source:http://pygments.org/demo/16998/

I think you forgot to put
from sympy import S

at the top.

 

Yes, thanks, I really miss it! I just remove it in the last moment before highlighting code.  

Did I get it right that you calculate the ground state energy of the
1D infinite potential well of width $a$ with a perturbation which is
 linear in $x$, up to second order in perturbation?

 

Yes, you are right. I try to calculate the ground state energy for that case what you describe.

 

I think in general your code is fine. What you might want to do is
- have V an operator
- same for the unpertubed Hamiltonian H
- being able to write those operators in matrix form in a particular
basis
- find the basis which diagonalizes H
- use this basis to represent H and V in matrix forms
- compute perturbation theory to first, second, etc. order by looking
up the matrix forms
- make it general enough to handle degenerate cases

I think some of this is possible already, but I haven't looked deeply
 into it.

Thanks, I'll look deeply, may be I'll find some solutions of this points.  I'll search methods to solve it in current SymPy state.

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[Aaron S. Meurer]

I don't think it's possible to delete a discussion on a public mailing list. But I think Google Groups has a bug where sometimes it does not show discussions when searching or when browsing for whatever reason. But they are still there (you can usually find them by doing a normal Google search).

Aaron Meurer

[weralwolf]

Problem was solved when I reconnect from other network. Because before
I haven't see any discussions after 22.03.11

[weralwolf]

Sorry, but due to unexpected error what happens to my yesterday I
think it will be more useful to continue this topic there:
http://groups.google.com/group/sympy/browse_thread/thread/ade9df0af84bd17c