Why the allowed (stationary) orbits correspond to those for which the orbital angular momentum of the electron is an integer multiple of $\hbar=\frac {h}{2\pi}$?
$$L=n\hbar$$
**Bohr Quantization rule of the angular momentum**
that leads to energy levels of the Hydrogen atom:
$$E\_n=-\frac {Z^2}{1+\frac {m\_e}{M\_p}} \frac {\Re}{n^2}$$

the question is **Why quantum numbers are natural numbers**? $$E=nh\nu$$
$$n=0,1,2,3....$$