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Quantum Mechanics

Spin and Discrete Outcomes

Atomic beams and magnetic spectra reveal angular momentum that cannot all be explained by electron orbits. The chapter follows the observations, the introduction of electron spin, and the two-component description used today.

Reading sequence

Section titled “Reading sequence”
  • Stern–Gerlach Experiment explains the beam-splitting experiment, the classical expectation, the observed two-valued result, and the modern spin-1/21/2 interpretation.
  • Space Quantization explains the historical language of discrete angular-momentum projections and its modern operator meaning.
  • Pauli Exclusion Principle follows the historical route from shell closure and anomalous spectra to the exclusion rule for complete electron states.
  • Electron Spin traces the introduction of intrinsic electron spin from anomalous spectra through Pauli theory and the Dirac preview.
  • Pauli Matrices in Historical Context explains why noncommuting two-by-two matrices became the natural language for spin-1/21/2 physics.
  • Magnetic Moments connects orbital and spin magnetic moments, g factors, Zeeman signatures, and the QED precision preview.
  • Zeeman Effect Revisited explains normal and anomalous magnetic splitting as historical evidence for angular momentum and spin.
  • Spin-Statistics Preview previews how spin labels, exchange symmetry, fermions, bosons, and Pauli exclusion connect to the relativistic theorem.

Put the ideas to work

Section titled “Put the ideas to work”

Begin with Stern–Gerlach and space quantization, then read electron spin and magnetic moments. Distinguish the angular momentum of a whole atom from that of one free electron. The next calculation is a spin-1/2 measurement followed by sequential measurements.

References

Section titled “References”
  • B. Friedrich and D. Herschbach, “Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics,” Physics Today 56, 53-59 (2003), DOI: 10.1063/1.1650229.
  • W. Gerlach and O. Stern, “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld,” Zeitschrift für Physik 9, 349-352 (1922), DOI: 10.1007/BF01326983.
  • J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed., Cambridge University Press, 2020.