[aleph_minus_one]

> The hydrogenoid atoms and ions, with a single electron, are the exception that proves the rule, because anything more complex cannot be computed accurately.

Rather: there is no known closed-form solution (and there likely won't be any).

[dgfl]

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.