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Re: Variable transformations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131443] Re: Variable transformations
  • From: "Kevin J. McCann" <kjm at KevinMcCann.com>
  • Date: Tue, 23 Jul 2013 17:20:26 -0400 (EDT)
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Here is some code that I think I found, but may have written, a long 
time ago.

First the Function. The key is the Nest, which takes care of the 
derivatives.

Clear[COV, DEQ, \[Psi], x, z, f, n]
COV::usage =
   "COV[DEQ,\[Psi],x,z,f] changes the independent variable in a \
differential equation from x to z where x=f[z]. \[Psi] is the \
dependent variable or
   		function we are solving for.";

COV[DEQ_, \[Psi]_, x_, z_,
   f_] := (DEQ /. {D[\[Psi][x], {x, n_Integer}] :>
      Nest[(D[#, z]/D[f, z]) &, \[Psi][z], n], \[Psi][x] :> \[Psi][z],
     x :> f}
   		)

Here is an example of the usage:

de = -(\[HBar]^2/(2 m)) \!\(
\*SubscriptBox[\(\[PartialD]\), \({x, 2}\)]\(\[Psi][x]\)\) +
   1/2 m \[Omega]^2 x^2 \[Psi][x] - e \[Psi][x]

COV[de, \[Psi], x, z, \[Alpha] z + \[Beta]]

Hope this helps,

Kevin


On 7/23/2013 4:43 AM, Nicholas Chisholm wrote:
> Say I have some differential equation in terms of the independent variable
>
> Thanks!
>



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