I would like to understand what are the ideas (or data) on which the famous scientist has based himself to arrive at such a fundamental principle for quantum mechanics.
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1$\begingroup$ See Pauli exclusion principle for an overview. $\endgroup$– Mauro ALLEGRANZAApr 20, 2018 at 12:52
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1$\begingroup$ See Michela Massimi (2005), Pauli's Exclusion Principle : The Origin and Validation of a Scientific Principle for details. $\endgroup$– Mauro ALLEGRANZAApr 20, 2018 at 12:53
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4$\begingroup$ I'm voting to close this question as off-topic because lack context. $\endgroup$– Mauro ALLEGRANZAApr 20, 2018 at 12:54
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1$\begingroup$ The key word is "spin and statistics theorem", though Pauli guessed the special case 10 years earlier, en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem $\endgroup$– Alexandre EremenkoApr 20, 2018 at 16:58
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There is a whole book dedicated exactly to this question:
Ian Duck, E.C.G. Sudarshan, Pauli and the spin-statistics theorem, World Scientific, 1997.
Very roughly speaking, the story is the following. Bohr's model did not explain the periodic table, namely the mysterious numbers 2, 8, 18 and 32... To fit these numbers (and also anomalous Zeeman's effect, and spectra of alkali metals), Stoner proposed that there exists a new quantum number which takes two values. (An important contribution was also made by Lande). Pauli's guess was that this number there must be a new quantum number for the electron which takes two values, and that two electrons in an atom cannot have all numbers the same. So originally this was just a guess. It explained the observed spectral lines, their splitting in the Zeeman effect and the periods of the periodic table. Later, with the development of relativistic quantum mechanics and field theory this guess was explained by the so-called spin-statistics theorem. Pauli acknowledged that his original guess was "pure combinatorics" and spent the next 30 years of his career to find deeper physical reasons. In 1940 he gave a proof of the theorem.
The book that I cited reproduces all relevant papers (in English!).
Another excellent exposition of the same story is S. Tomonaga, The story of spin, U. Chicago Press, 1997.
answered Apr 20, 2018 at 20:20