Quantization of surface polaritons

We derive the exact quantization of surface polarions on ionic crystals. We show there are two different methods: (1) classical theory and (2) quantum theory. They give different results and both results are different than what is used currently. We argue the quantum theory is the correct choice. We also derive the interaction potential between a charged particle that interacts with these surface polaritons and also interacts with the bulk polaritons.