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I am looking for a detailed exposition of the quantum computation of the Zeeman effect in spectra of atoms from which it would be clear that the spin 1/2 of electron is unavoidable.

As far as I understand the original motivation of Uhlenbeck and Goudsmit to introduce spin 1/2 of electron came exactly from this problem, see their paper “ Spinning Electrons and the Structure of Spectra” (1926). However the discussion in the paper is purely qualitative and contains no computations.

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  • $\begingroup$ Is the detailed exposition in Wikipedia sufficient? It has computations and diagrams of energy levels. $\endgroup$
    – Ghoster
    Nov 24, 2022 at 19:58

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If an electron does not spin, where does the idea of spin come from? How the spin was introduced?

All begun with the discover of a fine and hyperfine structure in the emission and absorption spectra of atoms and molecules. Slightly different energy levels for electrons in the same atomic shell of an atom where explained by Pauli:

The optical hyperfine structure was observed in 1881 by Albert Abraham Michelson. ... Wolfgang Pauli proposed the existence of a small nuclear magnetic moment in 1924.

Two years earlier it had already been shown that an inhomogeneous external magnetic field influences the magnetic dipole of the atom and deflects the atom.

The Stern–Gerlach experiment involves sending a beam of silver atoms through an inhomogeneous magnetic field and observing their deflection.
If the particle is treated as a classical spinning magnetic dipole, it will precess in a magnetic field because of the torque that the magnetic field exerts on the dipole.

In 1925, George Uhlenbeck and Samuel Goudsmit at Leiden University suggested the simple physical interpretation of a particle spinning around its own axis

One year before Pauli described a two-valuedness of two electrons of otherwise identical electrons in the same atom shell.

In 1924 Wolfgang Pauli introduced what he called a "two-valuedness not describable classically" associated with the electron in the outermost shell. This allowed him to formulate the Pauli exclusion principle, stating that no two electrons can have the same quantum state in the same quantum system.

Since 1897 the electron has been seen as an electrically charged particle (J. J. Thomson) and the discover of a magnetic moment lead to the following conclusion:

Particles with spin can possess a magnetic dipole moment, just like a rotating electrically charged body in classical electrodynamics.

A remark about how the interpretation could be different and what would change:

  • The electron is a charge AND an magnetic dipole
  • The deflection of moving electrons in an external magnetic field is accompanied be the emission of photons and this is the reason for the deflection.
  • The spin as a synonyms for the magnetic dipole moment describes the Pauli principle and all the other descriptions associated with spin.
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