Talk:Exactly solvable model

Integrability and Solubility are indeed different

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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 $\theta ,\phi$). One can show that the Hamiltionan of this system $H$ commutes with both $L^{2}$ and $L_{z}$, and also $L^{2}$ and $L_{z}$ commute mutually(any undergraduate quantum mechanics text will have this). The system has three degrees of freedom, and three conserved quantities $H$, $L^{2}$ and $L_{z}$. 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 $r^{2}$ 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)

Integrability and Solubility

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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)