0
$\begingroup$

I'm experiencing troubles in obtaining the result of an ordinary differential equation with a boundary condition at infinity. I write down

Limit[DSolve[{ψ''[r] + 2/r*ψ'[r] - κ^2*ψ[r] == 
    0, ψ[a/2] == Subscript[Psi, 0], ψ[M] == 0}, ψ[r], 
  r], M -> Infinity]

And obtain

\!\(\*UnderscriptBox[\(\[Limit]\), \(M \[Rule] ∞\)]\) {{\
ψ[r] -> (
    a E^((a κ)/2 - 
      r κ) (-E^(2 M κ) + E^(2 r κ)) Subscript[
     Psi, 0])/(2 (E^(a κ) - E^(2 M κ)) r)}}

Which is correct, but is not evaluated for the limit. How can I force Mathematica to evaluate this limit?

$\endgroup$
1
$\begingroup$

Trying to do to much at once.

ψ[r_] = ψ[r] /. 
  DSolve[{(ψ'')[r] + (2 Derivative[1][ψ][r])/ r - κ^2 ψ[r] == 0, ψ[a/2] == 
      Psi0, ψ[M] == 0}, ψ[r], r][[1]]

Limit[ψ[r], M -> ∞]

Simplify[%, {r > 0 && κ > 0 && a > 0 && Psi0 ∈ Reals}]
(*(a Psi0 E^(1/2 κ (a - 2 r)))/(2 r)*)

Subscripts are not a good idea and Mathematica cannot always perform every function on rules.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.