> It is like saying that discrete orbits of electron say nothing about quantization of associated EM potential.
That's right, they don't. There is no such thing as "quantization of EM potential". The electromagnetic field is quantized, if you're using quantum field theory, but in QFT there is no "EM potential". In non-relativistic QM, the EM potential term in the Hamiltonian is not quantized and does not exhibit quantum properties. Even in models which add relativistic corrections, such as the models used in the late 1940s to predict the Lamb shift, the "quantization of the EM field" only applies to the "quantum electromagnetic field" external to the atom; it does not apply to the EM potential due to the nucleus.
> the paper is pretty clear that position and motion of neutrons were primarily affected by gravitational field, and as result the neutron position got quantized
No, the neutron positions were not quantized "as a result" of the gravitational field. They are already quantized in the absence of a gravitational field, as shown by numerous previous experiments. The only thing this experiment shows, as I've already said, is that under appropriate conditions, you have to include the gravitational potential in the potential term in the Hamiltonian.
That's right, they don't. There is no such thing as "quantization of EM potential". The electromagnetic field is quantized, if you're using quantum field theory, but in QFT there is no "EM potential". In non-relativistic QM, the EM potential term in the Hamiltonian is not quantized and does not exhibit quantum properties. Even in models which add relativistic corrections, such as the models used in the late 1940s to predict the Lamb shift, the "quantization of the EM field" only applies to the "quantum electromagnetic field" external to the atom; it does not apply to the EM potential due to the nucleus.
> the paper is pretty clear that position and motion of neutrons were primarily affected by gravitational field, and as result the neutron position got quantized
No, the neutron positions were not quantized "as a result" of the gravitational field. They are already quantized in the absence of a gravitational field, as shown by numerous previous experiments. The only thing this experiment shows, as I've already said, is that under appropriate conditions, you have to include the gravitational potential in the potential term in the Hamiltonian.