Dear all,
This question have been asked before, but, unfortunately, I do not get the point of the answers. The script below defines an expression in the variable u(rho). In this expression, the u(rho) is substituted by a function g(rho) which is a product of three functions of rho. One of these, v(rho) is the defined to be a polynomial. When the expression is evaluated then only v(rho) is substituted. The derivatives v' and v'' are not substituted.
Please point out where I fail!
Best regards,
ChG
(* 3D oscillator
Clear all variables to get a pristine state
*)
ClearAll[Evaluate[Context[] <> "*"]]
(* Define symbolic variables *)
rho = \[Rho]
rho0 = Subscript[rho, 0]
rho2 = rho^2
(* Define the radial equation *)
expr = D[ u[rho], {rho,2} ] - (-1 + l* (l + 1)/rho2 + rho0^2*rho2) u[rho]
(* Substitute u with a (later defined) interpolating function v[rho] *)
eqn1 = FullSimplify[ expr /. u -> Function[ rho, rho^(l+1)*Exp[-rho0*rho^2/2] * v[rho] ] ]
(* Remove the common factors. v, v-prime and v-bis appear *)
eqn2=Part[eqn1,3]
(* Define v[rho] as a polynomial *)
v[rho] = With[ {Nx=3}, 1+Sum[ a[n]*rho^n, {n,1,Nx} ] ]
(* The v-prime and v-bis are not evaluated *)
eqn3=FullSimplify[eqn2]
