After the lecture today and some meetings, I was exhausted and decided to cancel the lecture tomorrow to get a chance to rest. I hope I will be back on Friday.
I think the answer to the problem today about the extra time dependent exponential in the operator of A is that it should be without this factor. This is because we are working with the solution of the wave equation rather than transforming the equation to the HO form (like we did for the simple model of the vibrating string in the beginning of the semester). The solution has of course the time dependent factor, but this appears when the equation is solved and is not in the equation of motion itself.
Joakim