Exciton wave functions in semi-infinite semiconductors: A check of the adiabatic approximation

Wannier-exciton wave functions in the effective-mass approximation are found for a semi-infinite solid in the presence of the ‘‘no escape’’ boundary condition. These wave functions, which are independent of the adiabatic approximation and are very accurate in the mass range 1≤$m_h$/$m_e$≤5, allow an analytical calculation of the optical response to be made. A check of exciton wave functions based on the adiabatic approximation is performed. Adiabatic wave functions are in agreement with nonadiabatic ones for mass values $m_h$/$m_e$≃5, if a very accurate solution of the relative electron-hole motion is carried out.