We report on microtube with double quantum well and large radius of curvature. Method for calculating the ground-state energy of light hole exciton and density of states confined in a square potential model that consist of a narrow well, which is produced by a symmetrical structure. The exciton trial function is taken as a product of the ground state wave functions of both the unbound electron and hole in the heterostructure, with an arbitrary correlation function that depends only on electron-hole separation. A renormalized Schrödinger equation for the correlation function is derived and coincides with the corresponding equation for a hydrogen atom in an effective and space-isotropic homogeneous. The binding energy of the ground state to an exciton in this heterostructure, the contribution to the energy given by the sublevels and the density of states is determined as a function of the width of the well, the aluminum concentration and confinement potential profile is obtained by solving the equation calculated by the variational model proposed.