Talk:Exactly solvable model

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Integrability and Solubility are indeed different

If I am reading correctly then the few sentences of this page imply that INTEGRABILITY=EXACTLY SOLVABILITY in general. Inorder to appreciate this these are two different concepts I give an example where model is integrable but not exactly soluble.

Time dependent Schrodinger equation in three dimensions:

For a time dependent Schrodinger equation in three dimensions with a spherically symmteric potential(which means that potential only depends on the radial co-ordinate r, and not on θ,φ). One can show that the Hamiltionan of this system H commutes with both L2 and Lz, and also L2 and Lz commute mutually(any undergraduate quantum mechanics text will have this). The system has three degrees of freedom, and three conserved quantities H, L2 and Lz. Hence this systems in the sense of Liouville is integrable. However, from our knowledge of partial differential equations we know that there are two potential namely r2 and \frac{1}{r} which this can be exactly solved. Hence, solubility is more strict condition than integrablity.

This is enough to show that INTEGRABILITY \neq EXACTLY SOLVABILITY in general.

Hence special care should be taken when talking about exactly soluble models.

--Physics vivek (talk) 15:00, 16 March 2008 (UTC)


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Integrability and Solubility

This point is clearly explained in the article Integrable systems, which contains all that the present article contains, and a lot more (including references, cross-references, etc). The present article is therefore both redundent and inadequate, and should be deleted.

R physicist (talk) 16:11, 16 March 2008 (UTC)