scholarly journals Half-integral quantum numbers in the theory of the stark effect and a general hypothesis of fractional quantum numbers

1924 ◽  
Vol 105 (734) ◽  
pp. 641-650 ◽  
Keyword(s):  
Stark Effect ◽  
Zeeman Effect ◽  
Fractional Quantum ◽  
General Hypothesis ◽  
Quantum Numbers ◽  
Considerable Success ◽  
Anomalous Zeeman Effect ◽  
Band Spectra ◽  
Fractional Quantum Numbers ◽  
Integral Quantum

1. Indications of the occurrence of fractional quantum numbers have already been found by Kratzer from a study of certain band spectra, and by Curtis in his experimental investigation of helium bands. Heisenberg has also employed half-integral numbers in a quantum theory of the anomalous Zeeman effect with considerable success. The fourth of the slightly extended quantum conditions recently suggested by W. Wilson and applied by the present writer to the Zeeman effect involves a fractional quantum number, as O. W. Richardson has pointed out. K. F. Niessen, in his work on the positively ionised hydrogen molecule, observes certain discontinuities in the energy graphs between symmetrical and asymmetrical models which strongly the occurrence of half-integral quantum orbits for the latter. He refrains, however, from making this assumption, on the ground that it would necessitate the adoption of half numbers in the somewhat allied case of the Stark effect.

scholarly journals The stark effect in the molecular spectrum of hydrogen

1935 ◽  
Vol 234 (734) ◽  
pp. 115-144 ◽  
Keyword(s):  
Electric Fields ◽  
Stark Effect ◽  
Experimental Information ◽  
Quantum Numbers ◽  
Extensive Analysis ◽  
New Information ◽  
High Fields ◽  
Band Spectra ◽  
Low Dispersion

In considerations of the effect of electric fields on band spectra one finds attention focussed on the secondary spectrum of hydrogen, which alone shows appreciable Stark effect. Following some rather limited observations by early writers, Kiuti has given a more extensive analysis under low dispersion but high fields. This has remained the standard reference in all but the blue and violet regions where MacDonald has given better resolutions, and has succeeded in correlating some of the observed patterns with theory. The rapid advances made by Richardson and others in the classification of the normal H 2 spectrum together with the recent publication by MacDonald of a complete theory for the Stark effect in H 2 have increased enormously the interest attached to further experimental information. In addition, the Stark patterns have been shown to depend upon the rotational quantum numbers, so that the possibility of obtaining new information which may be of assistance in the analysis of the spectrum must not be overlooked.

scholarly journals Fractional quantum numbers via complex orbifolds

2019 ◽  
Vol 109 (11) ◽  
pp. 2473-2484
Author(s):  
Varghese Mathai ◽  
Graeme Wilkin
Keyword(s):  
Fractional Quantum ◽  
Quantum Numbers ◽  
Fractional Quantum Numbers

scholarly journals Fractional Quantum Numbers on Solitons

1981 ◽  
Vol 47 (14) ◽  
pp. 986-989 ◽  
Author(s):  
Jeffrey Goldstone ◽  
Frank Wilczek
Keyword(s):  
Fractional Quantum ◽  
Quantum Numbers ◽  
Fractional Quantum Numbers

scholarly journals Time Ordering Effects on Hydrogen Zeeman-Stark Line Profiles in Low-Density Magnetized Plasmas

2010 ◽  
Vol 2010 ◽  
pp. 1-5 ◽  
Author(s):  
J. Rosato ◽  
D. Boland ◽  
M. Difallah ◽  
Y. Marandet ◽  
R. Stamm
Keyword(s):  
Stark Effect ◽  
Principal Quantum Number ◽  
Zeeman Effect ◽  
Magnetized Plasmas ◽  
Low Density ◽  
Stark Broadening ◽  
Simulation Code ◽  
Quantum Numbers ◽  
Balmer Lines ◽  
Hydrogen Lines

Stark broadening of hydrogen lines is investigated in low-density magnetized plasmas, at typical conditions of magnetic fusion experiments. The role of time ordering is assessed numerically, by using a simulation code accounting for the evolution of the microscopic electric field generated by the charged particles moving at the vicinity of the atom. The Zeeman effect due to the magnetic field is also retained. Lyman lines with a low principal quantum number n are first investigated, for an application to opacity calculations; next Balmer lines with successively low and high principal quantum numbers are considered for diagnostic purposes. It is shown that neglecting time ordering results in a dramatic underestimation of the Stark effect on the low-n lines. Another conclusion is that time ordering becomes negligible only when ion dynamics effects vanish, as shown in the case of high-n lines.

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