If you let the computer run for long enough, it will compute any atomic spectrum to arbitrary accuracy. Only QFT has non-divergent series, so at least in theory

If you let the computer run for long enough, it will compute any atomic spectrum to arbitrary accuracy. Only QFT has non-divergent series, so at least in theory we expect the calculations to converge. There’s an intrinsic physical limit to which you can resolve a spectrum, so arbitrarily many digits of precision aren’t exactly a worthy pursuit anyway.