On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part Two)

Anthony Duncan; Michel Janssen

Home/Archive/arXiv

arXiv · physics/0610193

On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part Two)

Anthony Duncan·Michel Janssen

View original source ↗Read source document ↗Export metadata ↓

Abstract

This is the second installment of a two-part paper on developments in quantum dispersion theory leading up to Heisenberg's "Umdeutung" paper. In telling this story, we have taken a paper by John H. Van Vleck as our main guide. In this second part we present the detailed derivations on which our narrative in the first part rests. The central result that we shall derive is the Kramers dispersion formula, which played a key role in the thinking that led to Heisenberg's "Umdeutung" paper. Closely following Van Vleck's pre-Umdeutung approach, we derive classical and construct quantum formulae for the dispersion, emission, and absorption of radiation both for the special case of a charged harmonic oscillator (sec. 5) and for arbitrary non-degenerate multiply-periodic systems (sec. 6). In sec. 7, we rederive the same results using modern quantum mechanics. In sec. 8 we bring together the main conclusions of our study.

Explore related subjects

physics.hist-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Anthony Duncan, Michel Janssen. 2006-10-23. On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part Two). https://arxiv.org/abs/physics/0610193

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Astrobiology and the Transformation of Scientific Epistemology

Astrobiology occupies an unusual position within the philosophy of science. Confronted with the n = 1 problem - having only a single example of life to study - it attempts to investigate life beyond Earth while relying entirely on Earth's biosphere as its reference point, a constraint that creates unique epistemic challenges. Unlike traditional sciences with clear predictive frameworks, astrobiology operates as what we might call a transient science: a discipline functioning without foundational certainties, relying predominantly on abductive reasoning, and confronting hypotheses that may remain untestable for decades. It is, in essence, a science of absence - of evidence, certainty, and analogy - where progress lies in refining conceptual and experimental tools to recognize unfamiliar forms of life. This positions astrobiology alongside emerging fields like artificial intelligence and cognitive science within a broader transformation of how scientific knowledge is constructed when dealing with phenomena that transcend direct empirical access.

physics.hist-ph↗

arXiv2026

The wavelength of light as Thomas Young invented it

This paper documents Thomas Young's invention of a concept which he alternately refers to as the ''magnitude'', ''breadth'', ''interval'' or ''length of an undulation'' of light. First, the paper highlights that Young was first to link some concept of a wavelength to a theory of optics and to assign a precise value to this length for each component of the colour spectrum. Then, it sets out an explanation of how Young made up these values. Finally, it examines the reasons why Young introduced an optical wavelength into his theory of light, insofar as these reasons might in turn shed light on why he was first to do so.

physics.hist-ph↗

arXiv2026

Before WIMPs: Neutrinos and the origins of particle dark matter

After four decades of null-results, the experimental quest to discover a dark matter particle ardently continues. While confidence in the leading candidate, the Weakly Interacting Massive Particle (WIMP), is waning, its explanatory success still shapes current experimental approaches and theoretical expectations - from underground detecting efforts in Europe, China, and the U.S. to modern theories of cosmic structure. This paper traces the origins of this particle-based paradigm to a critical predecessor: the neutrino-dominated universe. Proposed in the early 1970s as a solution to extra-galactic anomalies, neutrinos became the leading explanation of 'missing matter' following experimental hints of neutrino mass in 1980. Although short-lived, the model's coherent picture of cosmic evolution and structure formation set strong conceptual and methodological standards - providing critical impetus to the field of particle cosmology. Examining this history invites renewed reflection on how such past aims and expectations continue to guide dark matter inquiry today.

physics.hist-ph↗