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

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page

Tests of sunspot number sequences: 1. Using ionosonde data

More than 70 years ago it was recognised that ionospheric F2-layer critical frequencies [foF2] had a strong relationship to sunspot number. Using historic datasets from the Slough and Washington ionosondes, we evaluate the best statistical fits of foF2 to sunspot numbers (at each Universal Time [UT] separately) in order to search for drifts and abrupt changes in the fit residuals over Solar Cycles 17-21. This test is carried out for the original composite of the Wolf/Zürich/International sunspot number [R], the new “backbone” group sunspot number [RBB] and the proposed “corrected sunspot number” [RC]. Polynomial fits are made both with and without allowance for the white-light facular area, which has been reported as being associated with cycle-to-cycle changes in the sunspot number - foF2 relationship. Over the interval studied here, R, RBB, and RC largely differ in their allowance for the “Waldmeier discontinuity” around 1945 (the correction factor for which for R, RBB and RC is, respectively, zero, effectively over 20 %, and explicitly 11.6 %). It is shown that for Solar Cycles 18-21, all three sunspot data sequences perform well, but that the fit residuals are lowest and most uniform for RBB. We here use foF2 for those UTs for which R, RBB, and RC all give correlations exceeding 0.99 for intervals both before and after the Waldmeier discontinuity. The error introduced by the Waldmeier discontinuity causes R to underestimate the fitted values based on the foF2 data for 1932-1945 but RBB overestimates them by almost the same factor, implying that the correction for the Waldmeier discontinuity inherent in RBB is too large by a factor of two. Fit residuals are smallest and most uniform for RC and the ionospheric data support the optimum discontinuity multiplicative correction factor derived from the independent Royal Greenwich Observatory (RGO) sunspot group data for the same interval

Ultrafast optics with a mode-locked erbium fiber laser in the undergraduate laboratory

We describe an ultrafast optics laboratory comprising a mode-locked erbium fiber laser, autocorrelation measurements, and a free-space parallel grating dispersion compensation apparatus. The gain spectrum of Er fiber provides a broad bandwidth capable of supporting sub-100 fs pulses centered near a wavelength of 1550 nm. The fiber laser design used here produces a train of pulses at a repetition rate of 55 MHz with pulse duration as short as 108 fs. The pulse duration is measured with a homebuilt autocorrelator using a simple Michelson interferometer that takes advantage of the two-photon nonlinear response of a common silicon photodiode. To compensate for temporal stretching of the short pulse due to group velocity dispersion in the fiber, an apparatus based on a pair of parallel gratings is used for pulse compression. A detailed part that lists in the supplementary material includes previously owned and common parts used by the telecommunications industry, which helps decrease costs of the laboratory. This provides a cost-effective way to introduce the principles of ultrafast optics to undergraduate laboratories. © 2021 Author(s).12 month embargo; published online: 22 November 2021This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]