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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <kslfml$po0$1@smc.vnet.net>

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! >