Jordan's 1926 results

Heisenberg wrote in (1929), that ‘the existence of the electron’ is as unintelligible to the wave mechanical theory as the ‘existence of the light quantum’ to Maxwell's theory. The fundamental problem for the light quantum was how it could produce interference. The fundamental problem concerning electricity was how quantization of electric charge could be deduced from the Schrödinger wave function because, according to wave mechanics, the total charge on a body is e∫Ψ*Ψd3r. How could the volume integral of the product of two wave functions be an integer?

Pascual Jordan approached this problem in the Dreimänner-Arbeit of 1926, coauthored with Born and Heisenberg, in the section entitled ‘Coupled harmonic oscillators. Statistics of wave fields’ (Born, Heisenberg and Jordan, 1926 – see letter of Heisenberg to Pauli of 23 October 1926, which confirms that Jordan wrote this section, in Pauli, 1979). Here the line of development begun by Bohr's coupling mechanism is explored further. Jordan cited the investigations of Ehrenfest (1906) and of Debye (1910) noting that neither of these approaches could include the important problem of the ‘coupling of distant atoms’ because they are semiclassical, mixing classical wave-theoretical notions with light quanta. Consequently, as Einstein (1925) had recognized, although Debye's method leads to Planck's formula, it gives the wrong result for the mean square fluctuations of cavity radiation in a volume element, yielding, instead of the expected two-term result (wave–particle duality of light), only the wave contribution.