Can Quantum Mechanics accurately explain all atomic transitions?

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I'm doing an experiment on Bohr's theory. I used the Rydberg formula to calculate the line in Helium. However, there are some other lines that the Rydberg formula failed to explain. Some of the transitions involve other quantum numbers as well... I've heard that the new Quantum Mechanics have a way to calculate it very precisely, but I can't find the guide on the internet...Could someone help me...? Thank you very much ^^
 
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