On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle. Part one

Duncan, Anthony; Janssen, Michel

doi:10.1007/s00407-007-0010-x

Cited by 44 publications

(3 citation statements)

References 124 publications

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“…The improved accessibility of texts and the enlargement of electronic repositories have made it much easier to discover new connections, patterns and influences, and to unearth new stories and new characters. For instance, just when it seemed that we knew all that was worth knowing about Heisenberg's Umdeutung paper, Michel Janssen and Tony Duncan managed to demonstrate that the American physicist John Van Vleck came, very close to the same result (Duncan and Janssen, ,b). Van Vleck was working in Minnesota, a place not quite as glamorous as Göttingen, although he was able to ground his approach on the imposing American tradition of celestial mechanics.…”

Section: Sourcesmentioning

confidence: 99%

What Have the Historians of Quantum Physics Ever Done for Us?

Badino

2016

Centaurus

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Section: Sourcesmentioning

confidence: 99%

What Have the Historians of Quantum Physics Ever Done for Us?

Badino

2016

Centaurus

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“…In the mid-1920s, a number of physicists working on the old quantum theory became increasingly suspicious of the notion of electron orbits. In the transition from the old quantum theory to both matrix mechanics and wave mechanics, orbits were discarded altogether (see Duncan and Janssen (2007) for the case of matrix mechanics). What we have shown in this paper, using the account of the Stark effect in the old and the new quantum theory as a striking example, is that orbits had become highly problematic well before the developments of the mid-1920s.…”

Section: Conclusion: Stark Contrasts Between the Old And The New Quanmentioning

confidence: 99%

The trouble with orbits: The Stark effect in the old and the new quantum theory

Duncan¹,

Janssen²

2014

Studies in History and Philosophy of Science Part B: Studies in

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The old quantum theory and Schrödinger's wave mechanics (and other forms of quantum mechanics) give the same results for the line splittings in the firstorder Stark effect in hydrogen, the leading terms in the splitting of the spectral lines emitted by a hydrogen atom in an external electric field. We examine the account of the effect in the old quantum theory, which was hailed as a major success of that theory, from the point of view of wave mechanics. First, we show how the new quantum mechanics solves a fundamental problem one runs into in the old quantum theory with the Stark effect. It turns out that, even without an external field, it depends on the coordinates in which the quantum conditions are imposed which electron orbits are allowed in a hydrogen atom. The allowed energy levels and hence the line splittings are independent of the coordinates used but the size and eccentricity of the orbits are not. In the new quantum theory, this worrisome non-uniqueness of orbits turns into the perfectly innocuous non-uniqueness of bases in Hilbert space. Second, we review how the so-called WKB (Wentzel-Kramers-Brillouin) approximation method for solving the Schrödinger equation reproduces the quantum conditions of the old quantum theory amended by some additional half-integer terms. These extra terms remove the need for some arbitrary extra restrictions on the allowed orbits that the old quantum theory required over and above the basic quantum conditions. 1

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“…Instead, Jordan drew on the canonical formalism of classical mechanics. Jordan was steeped in this formalism, which had played a central role in the transition from the old quantum theory to matrix mechanics (Duncan and Janssen, 2007) as well as in the further development of the new theory, to which Jordan had made a number of significant contributions Janssen, 2008, 2009). Most importantly in view of the project Jordan pursued in Neue Begründung, he had published two papers the year before (Jordan, 1926a,b), in which he had investigated the implementation of canonical transformations in matrix mechanics (Lacki, 2004;Duncan and Janssen, 2009).…”

Section: Von Neumann's Mathematische Begründung (May 1927)mentioning

confidence: 99%

(Never) Mind your p’s and q’s: Von Neumann versus Jordan on the foundations of quantum theory

Duncan

Janssen

2012

EPJ H

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In two papers entitled "On a new foundation [Neue Begründung] of quantum mechanics," Pascual Jordan (1927b,g) presented his version of what came to be known as the Dirac-Jordan statistical transformation theory. As an alternative that avoids the mathematical difficulties facing the approach of Jordan and Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert space formalism of quantum mechanics. In this paper, we focus on Jordan and von Neumann. Central to the formalisms of both are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in quantum mechanics. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identification of sets of canonically conjugate variables, i.e., p's and q's. For von Neumann, not constrained by the analogy to classical mechanics, it required only the identification of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p's and q's. Jordan and von Neumann also stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan (1927b) was the first to state those rules in full generality. Von Neumann (1927a) rephrased them and, in a subsequent paper , sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics.

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On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle. Part one

Cited by 44 publications

References 124 publications

What Have the Historians of Quantum Physics Ever Done for Us?

What Have the Historians of Quantum Physics Ever Done for Us?

The trouble with orbits: The Stark effect in the old and the new quantum theory

(Never) Mind your p’s and q’s: Von Neumann versus Jordan on the foundations of quantum theory

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