- #1
Physicslad78
- 47
- 0
I am trying to solve the following differential equation:
where is the angular momentum given by:
goes from 0 to while goes from 0 to . w and k are constants and E is the energy of the system.. This differential equation is non separable. However i have realized that
I plugged that in differential equation above and multiplied the whole equation by and then used the integral properties of three spherical harmonics multiplied together (in terms of wigner 3 j symbols). This is to get a recursion relation between different coefficients found in the solution that I assumed :
I am looking at the case when m=1 hence the substitution by 1 for m in above equation. My two questions are: (1) How will I treat the term above contatining i? I only took the part without i and got solutions but some of the eigenvalues are complex (it is an energy term) so it is not possible! (2) even inserting i would cause more problems as u still get complex values..can anyone tell me what might be going wrong?.Thanks
Thanks
where is the angular momentum given by:
goes from 0 to
I plugged that in differential equation above and multiplied the whole equation by
I am looking at the case when m=1 hence the substitution by 1 for m in above equation. My two questions are: (1) How will I treat the term above contatining i? I only took the part without i and got solutions but some of the eigenvalues are complex (it is an energy term) so it is not possible! (2) even inserting i would cause more problems as u still get complex values..can anyone tell me what might be going wrong?.Thanks
Thanks
Last edited by a moderator: