= Born statistical scattering interpretation
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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.<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]{ref}
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.<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 https://studyres.com/doc/8624145/the-statistical-interpretation-of-quantum-mechanics, paragraphs from the bound-electron difficulty through inelastic scattering]{ref}
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.
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