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Boston studies in the philosophy of science

From the 1926 Wave Mechanics to a Second-Quantisation Theory: Schrödinger’s New Interpretation of Wave Mechanics and Microphysics in the 1950’s

Salvo D’Agostino

Published Jan 1, 2000• 1 citation
Publisher
DOI
10.1007/978-94-010-9034-6_13

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Schrödinger's work on wave mechanics in 1926 appears to have been driven by the idea that one could give a purely wave-theoretical description of matter. Key elements in this picture were the idea of particles as wave packets (Section 4.3) and the possible implications for the problem of radiation (Section 4.4). This pure wave theory, in contrast to de Broglie's work, did away with the idea of particle trajectories altogether (Section 4.5). The main conflict, however, was between Schrödinger and the proponents of quantum mechanics (in particular Heisenberg, Section 4.6), both in its form at the time of Schrödinger's papers and in its further developments as sketched in the previous chapter. For reference, we provide a brief chronology of Schrödinger's writings relating to wave mechanics up to the Solvay conference: Paper on Einstein's gas theory, submitted 15 December 1925, published 1 March 1926 (Schrödinger 1926a). First paper on quantisation, submitted 27 January 1926, addendum in proof 28 February 1926, published 13 March 1926 (Schrödinger 1926b). Second paper on quantisation, submitted 23 February 1926, published 6 April 1926 (Schrödinger 1926c). Paper on the relation between wave and matrix mechanics (‘equivalence paper’), submitted 18 March 1926, published 4 May 1926 (Schrödinger 1926d). Paper on micro- and macromechanics (coherent states for the harmonic oscillator), published 9 July 1926 (Schrödinger 1926e). […]
Abstract This chapter explores Schrödinger’s introduction of wave mechanics. After briefly covering Schrödinger’s earlier work, it turns to the investigations that led him to write a four-part paper in 1926 introducing and applying wave mechanics. The chapter provides a detailed analysis of these four papers, in which the analogy of the new theory to the Hamilton-Jacobi formulation of classical mechanics plays a central role, as well as the paper written in between the second and the third installment on the relation between wave and matrix mechanics. The chapter also discusses Schr "odinger’s original interpretation of his wave functions and the reception of his theory by the physics community.
Abstract In June 1925 Heisenberg made the breakthrough that would lead to matrix mechanics. The theory was abstract, offered no means for visualizing the mechanics of the atom, and its application required a lot of heavy lifting. Erwin Schrödinger subsequently made the breakthrough that would lead to wave mechanics, building on Louis de Broglie’s association of a wave with an electron. In Schrödinger’s wave equation the quantum numbers of the hydrogen atom arise naturally. He argued that his ‘wavefunction’ offered a realistic description of the electron in an atom, and sought to eliminate Bohr’s discontinuous quantum jumps. But in the spring of 1926, Max Born offered an enduring alternative. The modulus-square of the wavefunction is a measure of probability in an unvisualizable microphysics. In an intense debate with Bohr, Schrödinger demanded a theory based on logical concepts free from contradictions. Bohr was left to ponder what this might mean.