The concept of quantum numbers and their significance in atomic physics was developed and formulated by several scientists during the early 20th century. The foundational work was carried out by several physicists, including Arnold Sommerfeld, Wolfgang Pauli, and Niels Bohr.
In particular, Wolfgang Pauli played a significant role in the development of quantum numbers through his proposal of the Pauli exclusion principle. In 1925, Pauli postulated that no two electrons in an atom can have the same set of quantum numbers, which led to the understanding of electron configurations and the filling of electron shells.
Niels Bohr's atomic model, proposed in 1913, laid the groundwork for understanding the quantized energy levels of electrons in an atom. Bohr introduced the concept of stationary states, where electrons occupy specific energy levels or orbits around the nucleus, which are characterized by quantum numbers.
Arnold Sommerfeld, a student of Bohr, expanded upon his teacher's work and introduced additional quantum numbers to explain more complex atomic structures. Sommerfeld's contributions included the introduction of azimuthal quantum numbers, which described the shape of electron orbitals.
Overall, the discovery and development of quantum numbers were the result of the collective efforts of several physicists, with Wolfgang Pauli, Niels Bohr, and Arnold Sommerfeld playing significant roles in their formulation and understanding.