The numbers work: that means the model has not been faulted. With, of course, the data presented. Within the world of quantum mechanics, the model has proved extremely robust. It doesn't work at all outside it. Gravitation has (so far) refused to be helped.

As for a deeper understanding, that is something that generally comes about when the model fails. The CLASSIC case is Copernicus' realisation that the solar- centric system worked better than the Earth- centric model. But it took over 50 years to get the model to work, partly because of poor accuracy of observations before the telescope, and partly because Copernicus' model assumed perfect circles, whereas the orbits are ellipses. Tycho Brahe started the rectification of the first problem, with a humungous non- telescope observatory that got better accuracy; Kepler worked out the second, though it took right up to Newton to get it mathematically based.

I've often wondered what would have happened if Fourier analysis had been thought of in, say, 1520. All those epicycles would have become merely extra terms in an equation, and there would have been no incentive to improve the model. The fact that the fixed stars move so rapidly - their sphere, at vast distance, circled the Earth once a day- would have made the assumption of faster-than-light movement part of the model. Relativity would have been impossible.

I sometimes think quantum theory has got itself into this state. Maybe wave- oarticle duality is the modern equivalent of epicycles.