Chrysler Repair: Brake Noise, caliper piston, frequency oscillation

Question
I just replaced the disc brakes all around and put new rotors on the front. Now have a squealing noise when the brakes are first applied. Had the pads taken off, checked for dust, glazing and sanded the pads. Brakes work fine. Full pedal, no fade and sure breaking. Can't get rid of the noise. Car is a 200 Chrysler 300M.
Thanks for any help you can offer.

Answer
Hi Mike,
While I am an amateur, my experience with brake sqeal is that if there is any free play between the back of the pad and the caliper piston the pushes on it, or the same thing on the opposite side pad and caliper support, that sets up the possibility of high frequency oscillation. Several compounds are available to glue the back of the pad to its interfacing surface. One I have used is a spray can by Permatex called Disc Brake Quiet.
There are also brush on equivalent compounds but the spray on type goes on more evenly so may work better. It wasn't clear to me if you did this work yourself or had it done in a shop, but either way it should be done if it wasn't  in the original job.
Roland