A reliable determination of the line profiles of atomic hydrogen for physical conditions of cool white dwarfs requires a unified theory which takes into account both the singlet and triplet transitions contributing to Lyman alpha using accurate interaction potentials and radiative dipole transition moments. We show that multiple perturber effects have to be considered using the autocorrelation formalism. A comparison with experimental laboratory spectra of cool dense plamas also shows that indeed multiple H-perturbers are an important influence in the far wing extending to 3000 Å in the ultraviolet. Under cool dense white dwarf atmosphere conditions, multiple perturber collisions for the singlet states contribute more to the ultraviolet opacity than binary collisions of the triplet states.