From Osher Doctorow

Niels Bohr's model of the atom has now become the "black sheep" of
physics because of things like its failure to explicitly include
probability, and so Nonconformists like me should probably take a
second look at it for possible benefits.

A surprising thing happens when we look at Bohr's model of orbits in
more detail. It's an awfully good approximation under certain
scenarios. Like Quantum Field Theory (QFT) which partly succeeded it,
some of those approximations are quite a bit beyond the usual idea of
"chance".

There's something similar to this in mathematical Combinatorics and
Number Theory, where Fermat's Last Theorem is "too good to be true,"
and in fact its proof in the last 2 decades has left specialists
wondering about the deeper nature of numbers. Like discrete energy
levels in Bohr's model, Fermat's Last Theorem only holds for integers
(the discrete energy levels aren't necessarily integers, but the level
indices are). By the way, Fermat's Last Theorem is false when we
leave the integers.

Readers who look up the keywords "Bohr model" under Wolfram or
Wikipedia and Hyperphysics (or subtopics under the last mentioned) will
find quite a few hints that the model might be generalized to
non-discrete or continuous physics (Condensed Physics, for example)
with a great deal of care and attention. For example, if energy E_n
at level n is regarded as proportional to radius r or radius divided by
length of the total cubical region considered, then we get an
"interpolated" Bohr model. If the "interpolated" model corresponds to
nothing physical (and I don't agree that this is correct), then welcome
to the club with tachyons, monopoles, ghosts, virtual particles, and so
on now part of physics, not to mention complex analysis and Clifford
algebras.

If you want to go a bit deeper into the "shortcomings" of the Bohr
model with possible ideas for remedying them, look at Wikipedia's "Fine
structure", "Hyperfine structure," "Zeeman effect," Hyperphysics'
"Zeeman effect," "Transition probabilities and Fermi's golden rule,"
Wikipedia's "Spectral line," "Levy skew alpha-stable distribution,"
Wolfram's "Schrodinger equation," etc.

I'll try to continue this later.

Osher Doctorow