IAPhyscisit, and so far the various spectra have looked pretty continuous to me. That's mainly because in an electric or magnetic field, the spectral lines can be fuzzed in continuous steps. Of course that's just an approximation, because in that case we assume that electromagnetic fields are continuous themselves - which they aren't in second quantization.

My current education doesn't allow me to give more fundamental statements about it, I was just curious if there's a simple argument of which quantization in steps of the Planck length falls out.

But I guess we're way too far off-topic by now...