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Klein-Gordon in Spherical Coordinates

I need a help. I'm a new user in Mathematica. I need to solve Klein-Gordon in spherical coordinate like this 

\[Psi]''[r] + 2 /r \[Psi]'[r] + m^2 \[Psi][r] == -E^2 \[Psi][r]

with m is the mass of particle and E is the eigenvalue. The boundary conditions are 

\[Psi]'[0] == 1, \[Psi][0] == constant,  \[Psi]'[infinity] == 0, \[Psi][infinity] == 0

How is the code that I have to make?
POSTED BY: M. Fitrah Alfian R.S.
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POSTED BY: M. Fitrah Alfian R.S.

Thank you for the answer. I'll try :)
POSTED BY: M. Fitrah Alfian R.S.

This is the radial equation for a free particle. To solve:

In[3]:= DSolve[ \[Psi]''[r] + 2/r \[Psi]'[r] + 
   m^2 \[Psi][r] == -E^2 \[Psi][r], \[Psi][r], r]

Out[3]= {{\[Psi][r] -> (E^(-Sqrt[-E^2 - m^2] r) C[1])/r + (
    E^(Sqrt[-E^2 - m^2] r) C[2])/(2 Sqrt[-E^2 - m^2] r)}}

C[2]=0 to satisfy the boundary condition at infinity, C[1] can be determined by normalization.
POSTED BY: S M Blinder
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