Skip to content
Quantum Mechanics

Primary Papers Index

These selected original papers connect historical claims to the publications that made them. The tables identify the problem each paper addresses; the references give full publication details. If the notation is unfamiliar, begin with the linked explanation and return to the original argument afterward.

Publication dates need interpretation: Planck presented his radiation law in 1900, before the 1901 journal article indexed here; de Broglie’s thesis was defended in 1924 and published in 1925. Later reprints and translations may carry still other dates. Nobel lectures provide retrospective accounts.

Radiation and the quantum atom

Section titled “Radiation and the quantum atom”
Original source Question or result Read alongside
Planck, 1901, blackbody radiation Radiation law and energy elements in thermal equilibrium Planck’s Radiation Law
Einstein, 1905, light quanta Frequency-dependent energy transfer and photoelectric reasoning Einstein’s Light Quantum Hypothesis
Millikan, 1916, photoelectric measurements Precision tests of stopping potential versus frequency Millikan’s Photoelectric Measurements
Rutherford, 1911, nuclear atom Large-angle alpha scattering and concentrated central charge Rutherford Scattering
Bohr, 1913, atomic constitution Old quantum theory explanation of hydrogen spectral regularities Bohr Model
Compton, 1923, X-ray scattering Wavelength shift explained by photon–electron energy and momentum transfer Compton scattering
Franck and Hertz, 1914, inelastic collisions Periodic energy losses in mercury, later understood as discrete excitation Franck–Hertz Experiment

Matter waves, matrices, and probabilities

Section titled “Matter waves, matrices, and probabilities”
Original source Question or result Read alongside
de Broglie, 1925, published thesis Wavelength-momentum relation for material particles de Broglie Matter Waves
Heisenberg, 1925, reinterpretation paper Transition quantities and noncommuting structure Heisenberg’s Matrix Mechanics
Born and Jordan, 1925, matrix formulation Matrix mechanics and canonical commutation structure Born and Jordan’s Matrix Formulation
Dirac, 1927, transformation theory Transformation amplitudes connecting representations; distinct from his 1925 quantum-bracket paper Dirac’s Transformation Theory
Schrödinger, 1926, first eigenvalue paper Wave mechanics and bound-state eigenvalue methods Schrödinger’s Wave Mechanics
Born, 1926, collision paper Probability interpretation of wave amplitudes Born Rule History
Davisson and Germer, 1927, electron diffraction Reflection diffraction evidence for electron waves Davisson–Germer Experiment
G. P. Thomson and Reid, 1927, electron diffraction Transmission diffraction evidence for electron waves G. P. Thomson Experiment

Spin, statistics, and uncertainty

Section titled “Spin, statistics, and uncertainty”
Original source Question or result Read alongside
Gerlach and Stern, 1922, atomic beam splitting Directional quantization evidence Stern–Gerlach Experiment
Pauli, 1925, exclusion principle Nonclassical exclusion rule for atomic structure Pauli Exclusion Principle
Bose, 1924, photon counting Counting argument leading to Bose statistics Bose’s Counting Argument
Fermi, 1926, ideal gas; Dirac, 1926, many-particle states Fermionic occupation and antisymmetric-state reasoning Fermi–Dirac Statistics
Heisenberg, 1927, uncertainty Measurement limits and noncommuting quantities Uncertainty Historical Origin

Completeness and Bell tests

Section titled “Completeness and Bell tests”
Original source Question or result Read alongside
Einstein, Podolsky, and Rosen, 1935 Completeness, locality assumptions, and correlated systems EPR Argument
Schrödinger, 1935, cat argument Macroscopic-superposition concerns in the response to EPR Schrödinger’s Cat
Bell, 1964 Inequalities for local hidden-variable theories Bell Theorem Historical Turning Point and Bell Theorem
Clauser, Horne, Shimony, and Holt, 1969 Experimentally usable Bell inequality CHSH Inequality
Freedman and Clauser, 1972 Early optical Bell-test experiment Bell Inequality Experiments
Aspect, Dalibard, and Roger, 1982, changing analyzers Polarization correlations with time-varying analyzer settings Aspect Experiments
Hensen, Giustina, and Shalm and their respective collaborators, 2015 Experiments closing the major detection and locality loopholes under stated assumptions Loophole-Free Bell Tests

Distinguish the claim from its later formulation

Section titled “Distinguish the claim from its later formulation”

Planck and Einstein. Planck’s radiation calculation used energy elements in counting oscillator energies. Einstein’s 1905 argument attributed a localized quantum character to light itself. Reading both papers helps prevent the later photon concept from being projected unchanged into Planck’s calculation.

Born’s collision paper. The 1926 paper concerns scattering amplitudes. Its added correction specifies the squared modulus in the probability interpretation. The modern Born rule applies to arbitrary specified measurements; that general formulation should not be attributed verbatim to the first collision paper.

Bell and the experiments. Bell’s 1964 argument, the 1969 CHSH inequality, and the experimental papers have different roles. A mathematical bound follows from assumptions; an experiment estimates correlations with finite data and a particular apparatus. Read both before deciding which assumptions a result constrains. The changing-analyzer paper by Aspect, Dalibard, and Roger is distinct from Aspect, Grangier, and Roger’s earlier 1982 polarization-correlation paper.

Exercise

Section titled “Exercise”

An experiment estimates the CHSH combination as S=2.4S=2.4, while the relevant local hidden-variable bound is ∣S∣≤2|S|\leq2. Is the number alone enough to conclude that the experiment rules out the models used in the theorem? Identify two things the experimental paper must additionally establish.

Solution

The apparent violation must be statistically significant: finite samples can fluctuate beyond the bound. The apparatus and analysis must also justify applying the bound to the measured sample, including the treatment of missed detections, setting choices, and possible communication between the measurement stations. A significant violation with these conditions addressed rejects the conjunction of the relevant assumptions; it does not imply controllable faster-than-light signaling.

References

Section titled “References”
  • A. Aspect, J. Dalibard, and G. Roger, “Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers,” Physical Review Letters 49, 1804–1807, 1982, DOI: 10.1103/PhysRevLett.49.1804.
  • J. S. Bell, “On the Einstein Podolsky Rosen Paradox,” Physics Physique Fizika 1, 195–200, 1964, DOI: 10.1103/PhysicsPhysiqueFizika.1.195.
  • N. Bohr, “On the Constitution of Atoms and Molecules,” Philosophical Magazine 26, 1–25, 1913, DOI: 10.1080/14786441308634955.
  • M. Born and P. Jordan, “Zur Quantenmechanik,” Zeitschrift für Physik 34, 858–888, 1925, DOI: 10.1007/BF01328531.
  • M. Born, “Zur Quantenmechanik der Stoßvorgänge,” Zeitschrift für Physik 37, 863–867, 1926, DOI: 10.1007/BF01397477.
  • S. N. Bose, “Plancks Gesetz und Lichtquantenhypothese,” Zeitschrift für Physik 26, 178–181 (1924), doi:10.1007/BF01327326.
  • J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Physical Review Letters 23, 880–884, 1969, DOI: 10.1103/PhysRevLett.23.880.
  • A. H. Compton, “A Quantum Theory of the Scattering of X-rays by Light Elements,” Physical Review 21, 483–502 (1923), doi:10.1103/PhysRev.21.483.
  • C. Davisson and L. H. Germer, “Diffraction of Electrons by a Crystal of Nickel,” Physical Review 30, 705–740, 1927, DOI: 10.1103/PhysRev.30.705.
  • L. de Broglie, “Recherches sur la théorie des quanta,” Annales de Physique, 10th series, 3, 22–128 (1925), doi:10.1051/anphys/192510030022; thesis defended in Paris in 1924.
  • P. A. M. Dirac, “On the Theory of Quantum Mechanics,” Proceedings of the Royal Society A 112, 661–677 (1926), doi:10.1098/rspa.1926.0133.
  • P. A. M. Dirac, “The physical interpretation of the quantum dynamics,” Proceedings of the Royal Society A 113, 621–641 (1927), doi:10.1098/rspa.1927.0012.
  • A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Annalen der Physik 17, 132–148, 1905, DOI: 10.1002/andp.19053220607.
  • A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?,” Physical Review 47, 777–780, 1935, DOI: 10.1103/PhysRev.47.777.
  • E. Fermi, “Sulla quantizzazione del gas perfetto monoatomico,” Rendiconti della Reale Accademia Nazionale dei Lincei, series 6, 3, 145–149 (1926).
  • J. Franck and G. Hertz, “Über Zusammenstöße zwischen Elektronen und Molekülen des Quecksilberdampfes und die Ionisierungsspannung desselben,” Verhandlungen der Deutschen Physikalischen Gesellschaft 16, 457–467 (1914).
  • S. J. Freedman and J. F. Clauser, “Experimental Test of Local Hidden-Variable Theories,” Physical Review Letters 28, 938–941 (1972), doi:10.1103/PhysRevLett.28.938.
  • W. Gerlach and O. Stern, “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld,” Zeitschrift für Physik 9, 349–352 (1922), doi:10.1007/BF01326983.
  • M. Giustina et al., “Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons,” Physical Review Letters 115, 250401 (2015), doi:10.1103/PhysRevLett.115.250401.
  • W. Heisenberg, “Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen,” Zeitschrift für Physik 33, 879–893, 1925, DOI: 10.1007/BF01328377.
  • W. Heisenberg, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,” Zeitschrift für Physik 43, 172–198 (1927), doi:10.1007/BF01397280.
  • B. Hensen et al., “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015), doi:10.1038/nature15759.
  • R. A. Millikan, “A Direct Photoelectric Determination of Planck’s h,” Physical Review 7, 355–388 (1916), doi:10.1103/PhysRev.7.355.
  • W. Pauli, “Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren,” Zeitschrift für Physik 31, 765–783 (1925), doi:10.1007/BF02980631.
  • M. Planck, “Ueber das Gesetz der Energieverteilung im Normalspectrum,” Annalen der Physik 4, 553–563, 1901, DOI: 10.1002/andp.19013090310.
  • E. Rutherford, “The Scattering of α\alpha and β\beta Particles by Matter and the Structure of the Atom,” Philosophical Magazine 21, 669–688, 1911, DOI: 10.1080/14786440508637080.
  • E. Schrödinger, “Quantisierung als Eigenwertproblem,” Annalen der Physik 79, 361–376, 1926, DOI: 10.1002/andp.19263840404.
  • E. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik,” Naturwissenschaften 23, 807–812, 823–828, 844–849 (1935); first installment, doi:10.1007/BF01491891.
  • L. K. Shalm et al., “Strong Loophole-Free Test of Local Realism,” Physical Review Letters 115, 250402 (2015), doi:10.1103/PhysRevLett.115.250402.
  • G. P. Thomson and A. Reid, “Diffraction of Cathode Rays by a Thin Film,” Nature 119, 890 (1927), doi:10.1038/119890a0.