
We introduce the creation and annihilation operator b+ and b
and carrying out the unitary transformation
The ground state wave function of the system is Φ=φ(p)|0> We calculated the effective Hamiltonian and the renormalized mass of surface exciton by variational approach
.The result indicates that the self-trapping energy and the effective potential of a Wannier exciton can be written as a series in orJ, the first term being proportional to a, the coupling constant. The self-trapping energy and the effective potential not only includes the coupling contribution between the electron-hole and the different LO phonon branches,but also an extra contribution due to crossed terms between the different branches and the different wave vector virtual phonons, which is emitted via the excitonic recoil. The renormalized mass is obtained by Lagrange multiplier method. For Wannier exciton increasing part of the renormalized mass is proportional to a.