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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.^[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.^[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.

In 1925, Werner Heisenberg proposed replacing classical orbital quantities with arrays of transition amplitudes and frequencies. His paper's opening demanded relations between quantities observable in principle; section 1 built products by summing over an intermediate state and noted their dependence on order. The formulas above express that construction in modern linear operator notation.^[ref]

Pumping and a heated bath prepared Mercury vapor around a hot platinum wire, mesh and collector in the original Franck-Hertz experiment. A galvanometer read collector electric current while accelerating voltage varied at fixed retarding voltage. Retarding scans distinguished outgoing electron energies.^[ref] The losses constrain excitation of chemical atoms; they do not determine every optical coupling. The Franck-Hertz experiment explains the original mistaken ionization interpretation.

Such excitation and spectral line evidence motivated a mechanics of discrete energy levels and transitions. Replacing one representation by another was a theoretical construction; the Franck-Hertz experiment does not measure a matrix product or establish a unique representation of an observable.

Later in 1925, Max Born and Pascual Jordan developed the array calculus systematically. Their section 3 states $pq-qp=hI/(2\pi i)$, equivalently the modern canonical commutation relationThis relates position and momentum through an intrinsically noncommuting product.^[ref]

For the quantum harmonic oscillator, the canonical commutation relation and creation and annihilation operators give $H=\hslash \omega (a^{†}a+I/2)$, recovering both the spacing and zero-point energy algebraically. One must retain infinitely many number states for the exact relation: the finite cutoff below reveals the obstruction explicitly.

Homepage: www.nobelprize.org/prizes/physics/1954/born/facts/

Awarded in equal shares to Max Born for fundamental quantum mechanics research, especially the statistical interpretation of the wave function, and Walther Bothe for the coincidence circuit and discoveries made with it.^[ref]

A physicist who developed matrix mechanics and held a professorship in theoretical physics at Hamburg.^[ref]