Hi, I have been reading the Milonni and Eberly book "Laser": in one of the chapters they discuss the Oscillator Model. The treatment is quite straightforward, the Hamiltonian of the process is H=H0+HI where the first term is the "undisturbed" hamiltonian, and the second one is the interaction produced by an applied field. Φn are the eigenfunctions that solve the Schrödinger equation with HI=0 (i.e no applied field), but to continue you have to assume that the same functions (Φn) are also solutions to the problem when there is an applied field. How can you say that? What do you lose? Is there some kind of rule of thumb to be able to say that two problems (not necessarily these) will share eigenfunctions?