# Features of plasmon and surface plasmon polariton

What is the difference between surface plasmon polariton and plasmon in the Hamiltonian? So let's say that I can diagonalize the Hamiltonian of the system I am studying no matter how complicated that is, how do I distinguish a surface plasmon polariton from a bulk plasmon without plotting the charge of the wavefunction? Is there any auxiliary quantity that can be used? How are surface plasmons frequencies usually calculated in the quantum framework? (so no use of maxwell equations and dielectric constants allowed)

Thank you a lot