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Incoming links: The statistical interpretation of quantum mechanics by Max Born
Born statistical scattering interpretation 2026-10-18
The scattering interpretation connects an incoming preparation to the relative frequency of outgoing directions and final atomic states. Max Born's 1926 paper treats a distant incoming Electron and a chemical atom, expands the outgoing wavefunction into final atomic states, and imposes conservation of energy. Its translated correction footnote specifies the square of the coefficient; the modern complex modulus notation below is ours.[ref]
Zur Quantenmechanik der Stoßvorgänge by Max Born. Zur Quantenmechanik der Stoßvorgänge, 1926, pp. 863–867; inspected in D. H. Delphenich's translation, pp. 2–4, especially p. 3 equation (1) and footnote 1: squared coefficient
In his 11 December 1954 lecture, Max Born recalled the difficulty of interpreting bound Electrons alone. He instead described an incident Electron wave generating an outgoing spherical wave, with direction-dependent squared amplitude determining relative scattering probabilities. Distinct final atomic states describe excitation with corresponding Electron energy loss. This is a retrospective account of an interpretation, rather than the report of a new apparatus.[ref]
The statistical interpretation of quantum mechanics by Max Born. The statistical interpretation of quantum mechanics, lecture delivered 11 December 1954, printed pp. 261–262; inspected through the transcription at studyres.com/doc/8624145/the-statistical-interpretation-of-quantum-mechanics, paragraphs from the bound-electron difficulty through inelastic scattering
The distinction from the modern Born rule matters. The historical question was which collision outcome occurs: a direction of motion and a final atomic state. The general projective measurement formula applies to arbitrary observables, including degenerate outcomes and mixed states; a positive operator-valued measure describes still more general detector statistics. Those formulations should not be read back as the explicit contents of the short 1926 scattering paper. Nor does the scattering interpretation itself supply a rule for the conditional post-measurement state.
Actual experimental settings are described in the Davisson–Germer experiment and the Franck-Hertz experiment. The former scans collected electric current as an Electron beam scatters from prepared nickel; changing direction, accelerating voltage and surface preparation probes electron diffraction. The latter uses acceleration through mercury vapor and a retarding collector to infer discrete energy losses from current minima, with vapor density and retarding settings as controls. Angular resolution and surface backgrounds limit the first inference; initial energy spread and collision positions limit the second. These linked experiments supply the preparation, apparatus and readout; the examples below are original calculations, not Born's measured data.