Hello Bill, thank you so much for your answer.

About the '' yes, you are right, I noticed that a few minutes after posting this thread. About the mathematical problems, we have H[z] which does not have any derivative (there are no H[z]' ) and psi[z] which is a second derivative. The thing is that psi[z] depends on H[z] and vice-versa. About the boundary conditions, one of them (psi'[0]) depends on the result of NDSolve, which is psi[z].. So I really don't know how to solve complex system... If you have any idea that might help I'll really appreciate!

Thanks! :)