This number exceeds 100000 in a typical superconducting loop. Therefore its spectrum of the permitted states is strongly discrete: the energy difference between adjacent permitted states of a ring with a radius $r \approx 500 \ nm $ exceeds the value $\Delta E \approx N _{s}\hbar ^{2}/2mr^{2} \approx 2 \ 10^{-21} \ J$ corresponding to the temperature $T = \Delta E/k _{B} \approx 100 \ K$ at $N _{s} > 10^{5}$. The discreteness increases with the increase of all three sizes of the ring $\Delta E \approx N _{s}\hbar ^{2}/2mr^{2} \approx  n_{s}s2\pi r(\hbar ^{2}/2mr^{2}) \propto  (s/r)$ due to the increase of the number of Cooper pairs $N _{s}$.

The quantization of angular momentum postulated by Bohr may be deduced from the requirement that the complex wave function must be single-valued in any point $l$ of the loop $\Psi = |\Psi |e^{i\varphi } =  |\Psi |e^{i(\varphi + n2\pi )} $. The relation $$\oint_{l}dl \bigtriangledown \varphi = 2\pi n \eqno{(1)}$$ must be valid for any contour $l$ along which the wave function $\Psi = |\Psi |e^{i\varphi }$ is defined, according to this requirement. The angular momentum of each Cooper pair has a discrete value $n\hbar $ and the total angular momentum of 