Confinement of excitons in Quantum Dots

innovaterv

I am really really really confused how to approach this problem.
How exactly do you write the Hamiltonian for the behavior of excitons in Quantum Dots. Even if you assume your Quantum Dot to be an infinite potential well, is the system exactly solvable. Will a Center of Mass transformation help? Are you allowed to do that? Will not the potential become coupled?