I'm trying to solve (using the DSolve command) the following system
$\psi_1''[x]+(E_1-E-xV)\psi_1[x]-i\psi_2'[x]=0$
$\psi_2''[x]+(E_2-E-xV)\psi_2[x]-i\psi_1'[x]=0$
However, seems the Mathematica cannot manage to give a solution. Am I doing something wrong? Do you guys have any suggestions concerning some kind of transformation which will give a simpler equation to be solved?
DSolve[{ψ1''[x] + (-E1 - En - x V0) ψ1[x] - I ψ2'[x] == 0,
ψ2''[x] + (-E2 - En - x V0) ψ2[x] - I ψ1'[x] == 0}, {ψ1, ψ2}, x]
Thanks too much!
Best,